# Definition

Fibonacci sequence F(n), on the positive integers, are defined as such:

1. F(1) = 1
2. F(2) = 1
3. F(n) = F(n-1) + F(n-2), where n is an integer and n > 2


The Fibonacci-orial of a positive integer is the product of [F(1), F(2), ..., F(n)].

Given positive integer n, find the Fibonacci-orial of n.

# Specs

The fibonacci-orial of 100 must compute in under 5 seconds on a reasonable computer.

# Testcases

n   Fibonacci-orial of n
1   1
2   1
3   2
4   6
5   30
6   240
7   3120
8   65520
9   2227680
10  122522400
11  10904493600
12  1570247078400
13  365867569267200
14  137932073613734400
15  84138564904377984000
16  83044763560621070208000
17  132622487406311849122176000
18  342696507457909818131702784000
19  1432814097681520949608649339904000
20  9692987370815489224102512784450560000
100 3371601853146468125386964065447576689828006172937411310662486977801540671138589868616500834190029067583665182291701553172011082574587431382310099030394306877775647395167143332483560925112960024644459715300507481235056111434293619038347456390454209587101225261757371666449068625033999573552165524529725467628060170886602001077137613803027158648329335507728698605769992818756765633305318529965186184043999696650407246193257877568825245646129366994079739720698147440310773871269639752334356493678913424390564535389212240038895626811627949132978086070255082668392290037141141291484839596694182152062726390364094447642643912371532491388089634845995941928089653751672688740718152064107169357399466473375804972260594768969952507346694189050233823596316467570584434128052398891223730335019092974935617029638919358286124350711360361279157416837428904150054292406756317837582840596331363581207781793070936765786629772999832857257349696094416616259974304208756997835360702840912518532683324936435856348020736000000000000000000000000


# References

• – Leaky Nun Jul 30 '16 at 3:19
• @LuisMendo The sum of fibonacci is... you've guessed it, fibonacci. Well, minus one. – Leaky Nun Jul 30 '16 at 9:23
• @LeakyNun Currently the JavaScript answer only completes the test cases up to 15 because JavaScript cannot correctly compare (or manipulate) numbers beyond 2^53 - 1. This is most likely similar for a lot of the submissions here, because most languages don't support numbers that big – MayorMonty Jul 30 '16 at 13:54
• What do you mean by "reasonable computer"? – Erik the Outgolfer Jul 31 '16 at 16:26
• -1 because this seems like several challenges tacked together (range, fibonacci of each, factorial) with no particularly interesting shortcuts. – Esolanging Fruit Dec 28 '17 at 2:25

## Mathematica, 10 bytes

Fibonorial


Another Mathematica built-in soundly beaten by a golfing language without the built-in.

• I… w-what… why, Mathematica?! – Lynn Jul 30 '16 at 10:41
• Forgot that function even existed! – LegionMammal978 Jul 30 '16 at 13:42
• @Lynn Rule 35: If it exists, there's a Mathematica function of it ;) – Beta Decay Aug 3 '16 at 15:27
• @BetaDecay I thought we had established that it's Rule 110. – Martin Ender Aug 3 '16 at 15:29
• No, Rule 110 is something very different. Though I'm sure Mathematica has a built-in for that, too. – AdmBorkBork Aug 5 '16 at 19:05

# Jelly, 6 bytes

+Ð¡1ḊP


Input 100 finishes in 500 ms locally. Try it online!

### How it works

+Ð¡1ḊP  Niladic link. No input.

1    Yield 1.
+       Add the left and right argument.
Ð¡     Read a number n from STDIN.
Repeatedly call the dyadic link +, updating the right argument with
the value of the left one, and the left one with the return value.
Collect all values of the left argument into an array.
Ḋ   Dequeue; discard the first Fibonacci number (0).
P  Product; multiply the remaining ones.

• So is +¡1 a non-built in nth fibonacci and +Ð¡1 is the first n Fibonacci numbers? – caird coinheringaahing Oct 11 '17 at 22:02
• @cairdcoinheringaahing Pretty much. – Dennis Oct 11 '17 at 22:03
• I thought there was a built-in fibonacci function? – MilkyWay90 Mar 17 '19 at 17:20

# Actually, 4 bytes

Runs the input 100 within 0.2 seconds. Code:

R♂Fπ


Explanation:

R     # Get the range [1, ..., input].
♂F   # Map over the array with the fibonacci command.
π  # Take the product.


Uses the CP-437 encoding. Try it online!.

• This is the right tool for the job :) Thanks to some improvements to the Fibonacci function that Leaky Nun made a while back, the 100 test case runs in 0.1 seconds on TIO. – user45941 Aug 1 '16 at 2:27

## Brainfuck, 11981067817770741657611 603

,[>++++++[-<-------->]<<[->++++++++++<]>>,]>+>+>>+>+<<<<<<[->>>[[-]
<[->+<]>>[-<+<+>>]<[->+<[->+<[->+<[->+<[->+<[->+<[->+<[->+<[->+<[->
[-]>>>>>>+>+<<<<<<<<[->+<]]]]]]]]]]]+>>>>>>>>]<<<<<<<<[->[-<+<<+>>>
]<[->+<]>>>[<<<<<[->>>>>>>>+<<<<<<<<]>>>>>>>>>>>>>]<<<<<<<<[->>>[-<
<<<<<<<+>>>>[->+>>+<<<]>[-<+>]>>>]<<[->>>>>>>+>+<<<<<<<<]<+<<<<<<<<
]>>>[-]>>>>>[[-]>[->+<]>[-<+>[-<+>[-<+>[-<+>[-<+>[-<+>[-<+>[-<+>[-<
+>[->>>>>>+>+<<<<<<<<[-]]]]]]]]]]>]<<[<]+>>>>>>>>]<<<<<<<<[<<<<<<<<
]>>>>>[>>>>>>>>]+<<<<<<<<]>>>>>>>>>>>[<[-]>>[-<<+>>]>>>>>>>]<<<<<<<
<[<<<<<<<<]>>]>>>>>>[>>>>>>>>]<<<<<<<<[+++++[-<++++++++>]<.<<<<<<<]


# parse input (max 255)
,[>++++++[-<-------->]<<[->++++++++++<]>>,]
>+>+>>+>+<<<<<<
[->>>
# compute next fibonacci number
[[-]<
[->+<]>>
[-<+<+>>]<
# perform carries
[->+<[->+<[->+<[->+<[->+<[->+<[->+<[->+<[->+<
[->[-]>>>>>>+>+<<<<<<<<[->+<]]
]]]]]]]]]+>>>>>>>>
]<<<<<<<<
# multiplication
[->
# extract next digit of F_n (most significant first)
[-<+<<+>>>]<
[->+<]>>>
# move back to the end
[<<<<<
[->>>>>>>>+<<<<<<<<]>>>>>>>>>>>>>
]<<<<<<<<
# digit wise multiplication (shifting current digit)
[->>>
[-<<<<<<<<+>>>>
[->+>>+<<<]>
[-<+>]>>>
]<<
# shift previous total over one gap (in effect multiplying by 10)
[->>>>>>>+>+<<<<<<<<]<+<<<<<<<<
]>>>[-]>>>>>
# add product to total
[[-]>
[->+<]>
# perform carries
[-<+>
[-<+>[-<+>[-<+>[-<+>[-<+>[-<+>[-<+>[-<+>
[->>>>>>+>+<<<<<<<<[-]]
]]]]]]]]>
]<<[<]+>>>>>>>>
]<<<<<<<<
[<<<<<<<<]>>>>>
[>>>>>>>>]+<<<<<<<<
]>>>>>>>>>>>
# overwrite previous product
[<[-]>>
[-<<+>>]>>>>>>>
]<<<<<<<<
[<<<<<<<<]>>
]>>>>>>
# output product
[>>>>>>>>]<<<<<<<<
[+++++
[-<++++++++>]<.<<<<<<<
]


Try it online!

Runtime for n = 100 is less than 1 second with the online interpreter (about 0.2s locally using my own interpreter). Maximum input is 255, but would require the interpreter to support ~54000 cells (the online interpreter seems to wrap on 64k).

Change Log

Saved around 130 bytes with better extraction of the current digit to multiply through by, and by merging add and carry into a single pass. It also seems to be a bit faster.

Saved another 250 bytes. I managed to reduce my multiplication scratch pad by two cells, which saves bytes just about everywhere by not having to shift so far between digits. I also dropped the carry after multiplying through by a digit, and instead perform a full carry whilst adding to the running total.

Chopped another 50, again with better extraction of the current digit to multiply through by, simply by not moving it forward the first iteration, and working from where it is. A few micro-optimization further down account for around ~10 bytes.

30 more gone. Marking digits that have already been taken with a 0 rather than a 1 makes them easier to locate. It also makes the check if the multiplication loop has finished somewhat simpler.

I reduced the scratch pad by another cell, for 80 more bytes. I did this by merging the marker for the previous product and the current running total, which reduces the shifts between gaps, and makes bookkeeping a bit easier.

Saved another 50, by eliminating yet another cell, reusing the marker for fibonacci digits to mark the last digit taken as well. I was also able to merge the loop to shift the previous totals with the digit-wise multiplication loop.

Saved 8 bytes on input parsing. Oops.

## Python, 45 Bytes

a=b=o=1
exec"o*=a;a,b=b,a+b;"*input()
print o


Input is taken from stdin. Output for n = 100 finishes too quickly to accurately time. n = 1000 takes approximately 1s.

Sample Usage

$echo 10 | python fib-orial.py 122522400$ echo 100 | python fib-orial.py
3371601853146468125386964065447576689828006172937411310662486977801540671138589868616500834190029067583665182291701553172011082574587431382310099030394306877775647395167143332483560925112960024644459715300507481235056111434293619038347456390454209587101225261757371666449068625033999573552165524529725467628060170886602001077137613803027158648329335507728698605769992818756765633305318529965186184043999696650407246193257877568825245646129366994079739720698147440310773871269639752334356493678913424390564535389212240038895626811627949132978086070255082668392290037141141291484839596694182152062726390364094447642643912371532491388089634845995941928089653751672688740718152064107169357399466473375804972260594768969952507346694189050233823596316467570584434128052398891223730335019092974935617029638919358286124350711360361279157416837428904150054292406756317837582840596331363581207781793070936765786629772999832857257349696094416616259974304208756997835360702840912518532683324936435856348020736000000000000000000000000


## Haskell 41 29 Bytes

1+11 bytes saved by @Laikoni's remarks.

f=1:scanl(+)1f
(scanl(*)1f!!)


1,f and !! are separate tokens. The first lines defines the fibonacci sequence, the second is a function that computes the sequence of fibonacci-orials and returns the n-th for a given n. It starts printing digits almost immediately even for n=1000.

• You can get rid of the space (scanl(*)1f!!). – Laikoni Jul 30 '16 at 8:47
• And there is a shorter fibonacci generator here: f=1:scanl(+)1f – Laikoni Jul 30 '16 at 8:49
• @Laikoni That's amazing, thanks! – Christian Sievers Jul 30 '16 at 9:15
• @WillNess I think I am not only justified by what other users do, but also by meta.codegolf.stackexchange.com/questions/2419/… and meta.codegolf.stackexchange.com/questions/9031/… (but there is a lot more and I haven't read all) – Christian Sievers Aug 1 '16 at 11:07
• @flawr Would you accept 42+ as a function that adds 42? You shouldn't, because it is just an unfinished expression. But in Haskell we can add parentheses and get the section (42+), a way to write the function \n->42+n. Here it is the same, only with !! (the binary infix operator for indexing) instead of + and a more complicated first operand. – Christian Sievers Aug 5 '16 at 23:28

# Python 2, 39 bytes

f=lambda n,a=1,b=1:n<1or a*f(n-1,b,a+b)


Test it on Ideone.

• You may want to specify that it returns True in some cases. – Leaky Nun Jul 30 '16 at 17:19
• This would only return True for input 0, which isn't positive. – Dennis Jul 30 '16 at 17:22

# J, 17 16 bytes

1 byte is golfed with even better solution by miles.

[:*/+/@(!|.)\@i.


The idea is the same as the original but instead of forming the matrix to operate on minor diagonals we form the diagonals on the fly.

Original

To get the first n fibonomials:

*/\(#{.+//.)!/~i.


Reading right to left...
Create the array of consecutive integers (i.) up to specified one, from that array create the table (/~) of binomial coefficients (!) calculated from every pair in the array, this table is Pascal's triangle top of whlocated at the end of the first row and all elements under the main diagonal are 0, thankfully to implementation of !. If you sum (+/) all minor diagonals (/.), you get Fibonacci numbers, but you need to take ({.) as much of first elements from the resulting array as the length (#) of the table itself. Then the product (*/) applied to consecutive prefixes (\) of the array results into desired sequence of fibonorials. If you wish you can take only the last one using 2 more bytes ({:) but I thought that displaying all of them is not a sin :).
NB. the previous code block is not a J function.

   {:*/\(#{.+//.)!/~i. 10
122522400


For big numbers in J you use x at the end:

   {:*/\(#{.+//.)!/~i. 100x
3371601853146468125386964065447576689828006172937411310662486977801540671138589868616500834190029067583665182291701553172011082574587431382310099030394306877775647395167143332483560925112960024644459715300507481235056111434293619038347456390454209587101225...


The program runs on avarage 0.11s.

   100 timex '{:*/\(#{.+//.)!/~i.100x'
0.112124

• An alternative that is a function is [:*/+/@(!|.)\@i. using 16 bytes. It forms that same binomial coefficients along the table you generate using !/~ except that it forms that by taking prefixes of i.. – miles Jul 30 '16 at 23:06

# Pyth, 13 bytes

u*Gs=[sZhZ)Q1


Demonstration

This employs a clever, non-typesafe trick. Five of the characters (u*G ... Q1) say that the output is the product of the input many numbers. The rest of the code generates the numbers.

=[sZhZ) updates the variable Z to the list [s(Z), h(Z)]. Then s sums that list, to be multiplied.

Z is initially 0. s, on ints, is the identity function. h, on its, is the + 1 function. So on the first iteration, Z becomes [0, 1]. s on lists is the sum function, as mentioned above. h is the head function. So the second iteration is [1, 0].

Here's a list:

Iter  Z          Sum
0     0          Not used
1     [0, 1]     1
2     [1, 0]     1
3     [1, 1]     2
4     [2, 1]     3
5     [3, 2]     5


These sums are multiplied up to give the result.

# Mathematica 25 24 bytes

With thanks to Martin Ender.

1##&@@Fibonacci@Range@#&


1##&@@Fibonacci@Range@#&@100


Timing: 63 microseconds.

{0.000063,
3371601853146468125386964065447576689828006172937411310662486977801540
6711385898686165008341900290675836651822917015531720110825745874313823
1009903039430687777564739516714333248356092511296002464445971530050748
1235056111434293619038347456390454209587101225261757371666449068625033
9995735521655245297254676280601708866020010771376138030271586483293355
0772869860576999281875676563330531852996518618404399969665040724619325
7877568825245646129366994079739720698147440310773871269639752334356493
6789134243905645353892122400388956268116279491329780860702550826683922
9003714114129148483959669418215206272639036409444764264391237153249138
8089634845995941928089653751672688740718152064107169357399466473375804
9722605947689699525073466941890502338235963164675705844341280523988912
2373033501909297493561702963891935828612435071136036127915741683742890
4150054292406756317837582840596331363581207781793070936765786629772999
8328572573496960944166162599743042087569978353607028409125185326833249
36435856348020736000000000000000000000000}

• Alternately, with same byte count: 1##&@@Fibonacci~Array~#& – Greg Martin Jan 5 '17 at 19:18

# Jelly, 8 bytes

RḶUc$S€P  My first submission in Jelly. It's not as short as @Dennis' answer, but its only 2 bytes longer with a different method. Locally, it requires about 400ms compared to 380ms with @Dennis' version for n = 100. Try it online! ### Explanation RḶUc$S€P  Input: n
R         Generate the range [1, 2, ..., n]
For each value x in that range
Ḷ          Create another range [0, 1, ..., x-1]
U         Reverse that list
c        Compute the binomial coefficients between each pair of values
$Bind the last two links (Uc) as a monad S€ Sum each list of binomial coefficients This will give the first n Fibonacci numbers P Take the product of those to compute the nth Fibonacci-orial  # R, 99967876 66 bytes This answer is uses Binet's Formula, as well as the prod(x)function. Since R doesn't have a build-in Phi value, I defined it myself : p=(1+sqrt(5))/2;x=1;for(n in 1:scan())x=x*(p^n-(-1/p)^n)/sqrt(5);x  It works under 5 seconds, but R tends to give Inf as an answer for those big numbers... Ungolfed : r=sqrt(5) p=(1+r)/2 x=1 for(n in 1:scan()) x=x*(p^n-(-1/p)^n)/r x  -2 bytes thanks to @Cyoce ! Oh, do I love this site ! -10 bytes thanks to @user5957401 • Might be able to save a bit by storing sqrt(5) to a variable – Cyoce Aug 7 '16 at 6:20 • since you only use N once, you can just call scan inside the 1:N bit. i.e. for(n in 1:scan()). You can also save a few characters by just using * instead of the prod() function in your for loop. Your for loop is only one line, so you don't need the curly braces either. – user5957401 Aug 10 '16 at 19:31 • Nice idea to use Binet's formula. In your spirit but only 53 bytes is function(n,N=1:n,p=5^.5)prod(((1+p)^N-(1-p)^N)/2^N/p) – Michael M Feb 19 '18 at 9:19 # R, 82, 53, 49 bytes (48 bytes w/ different input style) b=d=1;a=0;for(i in 1:scan()){d=d*b;b=a+b;a=b-a};d  If we can just precede the code with the input number, we get the 48 byte ->n;b=d=1;a=0;for(i in 1:n){d=d*b;b=a+b;a=b-a};d  EDIT: New code. Original is below: a=function(n)ifelse(n<3,1,{v=c(1,1,3:n);for(i in 3:n)v[i]=v[i-1]+v[i-2];prod(v)})  Won't return anything other than Inf for a(100) though. And it won't work for anything but non-negative integers. Ungolfed: a=function(n){ if(n<3) return(1) v=c(1,1,3:n) for(i in 3:n) v[i]=v[i-1]+v[i-2] prod(v) }  ## PARI/GP, 29 bytes f=n->prod(i=1,n,fibonacci(i))  Or alternatively: f=n->prod(i=a=!b=0,n,b=a+a=b)  # Brachylog, 31 bytes ,[1:0]:?:{hH,?bh:H+g:?c.}irbb*.  Try it online! # Ruby, 39 bytes ->n{f=i=b=1;n.times{f,i,b=i,f+i,b*f};b}  • 36: ->n{f=i=b=1;n.times{b*=f;i=f+f=i};b} – G B Feb 23 '18 at 9:19 # Java, 165 bytes Golfed: BigInteger f(int n){BigInteger[]a={BigInteger.ZERO,BigInteger.ONE,BigInteger.ONE};for(int i=0;i<n;){a[++i%2]=a[0].add(a[1]);a[2]=a[2].multiply(a[i%2]);}return a[2];}  This is yet another case where BigInteger being required due to large numbers. However, I was able to keep the text BigInteger to a minimum, keeping the size down. I also compared with static imports, and it made the total length longer. This program works by tracking three numbers in an array. The first two are the previous two Fibonacci numbers. The third is the accumulated value. The loop starts out by calculating the next value and storing it in alternating (0, 1, 0, 1, ...) array indices. This avoids needing to shift values with costly (in terms of source size) assignment operations. Then grab that new value and multiply it into the accumulator. By avoiding temporary objects and limiting the loop to two assignment operators, I was able to squeeze out quite a few bytes. Ungolfed: import java.math.BigInteger; public class Fibonacci_orial { public static void main(String[] args) { // @formatter:off String[][] testData = new String[][] { { "1", "1" }, { "2", "1" }, { "3", "2" }, { "4", "6" }, { "5", "30" }, { "6", "240" }, { "7", "3120" }, { "8", "65520" }, { "9", "2227680" }, { "10", "122522400" }, { "11", "10904493600" }, { "12", "1570247078400" }, { "13", "365867569267200" }, { "14", "137932073613734400" }, { "15", "84138564904377984000" }, { "16", "83044763560621070208000" }, { "17", "132622487406311849122176000" }, { "18", "342696507457909818131702784000" }, { "19", "1432814097681520949608649339904000" }, { "20", "9692987370815489224102512784450560000" }, { "100", "3371601853146468125386964065447576689828006172937411310662486977801540671138589868616500834190029067583665182291701553172011082574587431382310099030394306877775647395167143332483560925112960024644459715300507481235056111434293619038347456390454209587101225261757371666449068625033999573552165524529725467628060170886602001077137613803027158648329335507728698605769992818756765633305318529965186184043999696650407246193257877568825245646129366994079739720698147440310773871269639752334356493678913424390564535389212240038895626811627949132978086070255082668392290037141141291484839596694182152062726390364094447642643912371532491388089634845995941928089653751672688740718152064107169357399466473375804972260594768969952507346694189050233823596316467570584434128052398891223730335019092974935617029638919358286124350711360361279157416837428904150054292406756317837582840596331363581207781793070936765786629772999832857257349696094416616259974304208756997835360702840912518532683324936435856348020736000000000000000000000000" } }; // @formatter:on for (String[] data : testData) { System.out.println("Input: " + data[0]); System.out.println("Expected: " + data[1]); System.out.print("Actual: "); System.out.println(new Fibonacci_orial().f(Integer.parseInt(data[0]))); System.out.println(); } } // Begin golf BigInteger f(int n) { BigInteger[] a = { BigInteger.ZERO, BigInteger.ONE, BigInteger.ONE }; for (int i = 0; i < n;) { a[++i % 2] = a[0].add(a[1]); a[2] = a[2].multiply(a[i % 2]); } return a[2]; } // End golf }  Program output: Input: 1 Expected: 1 Actual: 1 Input: 2 Expected: 1 Actual: 1 Input: 3 Expected: 2 Actual: 2 Input: 4 Expected: 6 Actual: 6 Input: 5 Expected: 30 Actual: 30 Input: 6 Expected: 240 Actual: 240 Input: 7 Expected: 3120 Actual: 3120 Input: 8 Expected: 65520 Actual: 65520 Input: 9 Expected: 2227680 Actual: 2227680 Input: 10 Expected: 122522400 Actual: 122522400 Input: 11 Expected: 10904493600 Actual: 10904493600 Input: 12 Expected: 1570247078400 Actual: 1570247078400 Input: 13 Expected: 365867569267200 Actual: 365867569267200 Input: 14 Expected: 137932073613734400 Actual: 137932073613734400 Input: 15 Expected: 84138564904377984000 Actual: 84138564904377984000 Input: 16 Expected: 83044763560621070208000 Actual: 83044763560621070208000 Input: 17 Expected: 132622487406311849122176000 Actual: 132622487406311849122176000 Input: 18 Expected: 342696507457909818131702784000 Actual: 342696507457909818131702784000 Input: 19 Expected: 1432814097681520949608649339904000 Actual: 1432814097681520949608649339904000 Input: 20 Expected: 9692987370815489224102512784450560000 Actual: 9692987370815489224102512784450560000 Input: 100 Expected: 3371601853146468125386964065447576689828006172937411310662486977801540671138589868616500834190029067583665182291701553172011082574587431382310099030394306877775647395167143332483560925112960024644459715300507481235056111434293619038347456390454209587101225261757371666449068625033999573552165524529725467628060170886602001077137613803027158648329335507728698605769992818756765633305318529965186184043999696650407246193257877568825245646129366994079739720698147440310773871269639752334356493678913424390564535389212240038895626811627949132978086070255082668392290037141141291484839596694182152062726390364094447642643912371532491388089634845995941928089653751672688740718152064107169357399466473375804972260594768969952507346694189050233823596316467570584434128052398891223730335019092974935617029638919358286124350711360361279157416837428904150054292406756317837582840596331363581207781793070936765786629772999832857257349696094416616259974304208756997835360702840912518532683324936435856348020736000000000000000000000000 Actual: 3371601853146468125386964065447576689828006172937411310662486977801540671138589868616500834190029067583665182291701553172011082574587431382310099030394306877775647395167143332483560925112960024644459715300507481235056111434293619038347456390454209587101225261757371666449068625033999573552165524529725467628060170886602001077137613803027158648329335507728698605769992818756765633305318529965186184043999696650407246193257877568825245646129366994079739720698147440310773871269639752334356493678913424390564535389212240038895626811627949132978086070255082668392290037141141291484839596694182152062726390364094447642643912371532491388089634845995941928089653751672688740718152064107169357399466473375804972260594768969952507346694189050233823596316467570584434128052398891223730335019092974935617029638919358286124350711360361279157416837428904150054292406756317837582840596331363581207781793070936765786629772999832857257349696094416616259974304208756997835360702840912518532683324936435856348020736000000000000000000000000  # Javascript (ES6), 51 39 bytes Recursive implementation (39 bytes) f=(n,a=p=i=b=1)=>++i<n?f(n,b,p*=b+=a):p  Original implementation (51 bytes) n=>{for(i=a=b=p=1;++i<n;){c=a;a=b;p*=b+=c}return p}  Note: Starts rounding errors for the Fibonacci-orial of 16, 100 is just Infinity, runs in what appears to be <1 second. • I made an alternate 53-byte version n=>[...Array(n)].reduce(p=>(c=a,a=b,p*=b+=c),a=1,b=0) only to discover that you'd counted the f= which isn't required saving you 2 bytes. – Neil Jul 30 '16 at 9:00 • Fair point. My rationale was so it was callable and reusable rather than just callable. – Pandacoder Jul 30 '16 at 13:38 • Sure, but if someone does want to reuse it then they still have the option of naming it. – Neil Jul 30 '16 at 20:08 • @Neil Well now I went and re-implemented it and now the f= is mandatory or else it can't actually execute. :D – Pandacoder Aug 15 '16 at 22:18 • Well at least you fixed the byte count for the original implementation. – Neil Aug 15 '16 at 22:53 # DC (GNU or OpenBSD flavour), 36 bytes File A003266-v2.dc: 0sA1sB1?[1-d0<LrlBdlA+sBdsA*r]dsLxrp  (no trailing newline) ...now the result is held on the stack instead of using a named register (is Y in version 1). The r command is not available in the original dc (see RosettaCode's Dc page). Run: $ time dc -f A003266-v2.dc <<< 100
337160185314646812538696406544757668982800617293741131066248697780154\
067113858986861650083419002906758366518229170155317201108257458743138\
231009903039430687777564739516714333248356092511296002464445971530050\
748123505611143429361903834745639045420958710122526175737166644906862\
503399957355216552452972546762806017088660200107713761380302715864832\
933550772869860576999281875676563330531852996518618404399969665040724\
619325787756882524564612936699407973972069814744031077387126963975233\
435649367891342439056453538921224003889562681162794913297808607025508\
266839229003714114129148483959669418215206272639036409444764264391237\
153249138808963484599594192808965375167268874071815206410716935739946\
647337580497226059476896995250734669418905023382359631646757058443412\
805239889122373033501909297493561702963891935828612435071136036127915\
741683742890415005429240675631783758284059633136358120778179307093676\
578662977299983285725734969609441661625997430420875699783536070284091\
2518532683324936435856348020736000000000000000000000000

real    0m0.005s
user    0m0.004s
sys     0m0.000s


Trying to explain:

tos is the contents of the top of the stack without removing it.
nos is the element below tos.

0 sA # push(0) ; A=pop()
1 sB # push(1) ; B=pop()
1    # push(1)
# this stack position will incrementally hold the product
?    # push( get user input and evaluate it )
[    # start string
1-  # push(pop()-1)
d   # push(tos)
0   # push(0)
<L  # if pop() < pop() then evaluate contents of register L
r   # exchange tos and nos
# now nos is the loop counter
# and tos is the bucket for the product of the fibonacci numbers
lB  # push(B)
d   # push(tos)
lA  # push(A)
+   # push(pop()+pop())
# now tos is A+B, nos still is B
sB  # B=pop()
# completes B=A+B
d   # push(tos)
sA  # A=pop()
# completes B=A
# tos (duplicated new A from above) is the next fibonacci number
*   # push(nos*tos)
# tos now is the product of all fibonacci numbers calculated so far
r   # exchange tos and nos
# now tos is the loop counter, nos is the product bucket
]    # end string and push it
d    # push(tos)
sL   # L=pop()
x    # evaluate(pop())
r    # exchange tos and nos
# nos now is the former loop counter
# tos now is the complete product. \o/
p    # print(tos)
# this does not pop() but who cares? :-P


# DC, 41 bytes

...straight forward, no tricks:

File A003266-v1.dc:

0sA1sB1sY?[1-d0<LlBdlA+sBdsAlY*sY]dsLxlYp


(no trailing newline)

Run:

$for i in$(seq 4) ; do dc -f A003266-v1.dc <<< $i ; done 1 1 2 6$ time dc -f A003266-v1.dc <<< 100
337160185314646812538696406544757668982800617293741131066248697780154\
067113858986861650083419002906758366518229170155317201108257458743138\
231009903039430687777564739516714333248356092511296002464445971530050\
748123505611143429361903834745639045420958710122526175737166644906862\
503399957355216552452972546762806017088660200107713761380302715864832\
933550772869860576999281875676563330531852996518618404399969665040724\
619325787756882524564612936699407973972069814744031077387126963975233\
435649367891342439056453538921224003889562681162794913297808607025508\
266839229003714114129148483959669418215206272639036409444764264391237\
153249138808963484599594192808965375167268874071815206410716935739946\
647337580497226059476896995250734669418905023382359631646757058443412\
805239889122373033501909297493561702963891935828612435071136036127915\
741683742890415005429240675631783758284059633136358120778179307093676\
578662977299983285725734969609441661625997430420875699783536070284091\
2518532683324936435856348020736000000000000000000000000

real    0m0.006s
user    0m0.004s
sys     0m0.004s

• *sigh!* ... writing dc code definitely is easier than explaining it... – user19214 Aug 1 '16 at 12:05
• Yeah, we really need an IDE with some kind of crazy multiple-stack visualisation gadget... that would be sweet. – Joe Aug 1 '16 at 15:13
• I have several ideas what to add as new commands, but the idea with the highest impact seems to be: Add a "change default stack" command. ;-) – user19214 Aug 1 '16 at 17:23
• ...or swap default stack with a named register. That would make more knots in users' brains but would not need the default stack to have a name... ]:-) – user19214 Aug 1 '16 at 17:29
• Yes, that would definitely be handy! I'd also like to clear a single item, rotate items that aren't at the top of the stack, and maybe shift the top n items to another stack at once. For now, though, I still don't know how to compile dc from source. :/ – Joe Aug 6 '16 at 5:21

# C# 110109107103101 94 Bytes

using i=System.Numerics.BigInteger;i f(i n){i a=0,b=1,x=1;for(;n-->0;)x*=a=(b+=a)-a;return x;}


## Explanation

//Aliasing BigInteger saves a few bytes
using i=System.Numerics.BigInteger;

//Since BigInteger has an implicit from int we can also change the input
//and save two more bytes.
i f(i n)
{
//using an alternative iterative algorithm (link to source below) to cut out the temp variable
//b is next iteration, a is current iteration, and x is the running product
i a = 0, b = 1, x = 1;

//post decrement n down to zero instead of creating a loop variable
for (; n-- > 0;)

//The bracket portion sets the next iteration
//get the current iteration and update our running product
x *= a = (b += a) - a;

return x;
}


Iterative Fib algorithm

• Given this performed so much better than I had expected I wanted to find the max N that would return in under 5 seconds, I came out with 1540 which gives a number that is 247441 digits long. – user19547 Aug 11 '16 at 23:36
• Impressive. How long does 1541 take to calculate, out of curiosity? – Pandacoder Aug 15 '16 at 22:25
• @Pandacoder So with the recent change to the algorithm it has gotten significantly faster. 1541 in 755 ms so i'm going to find the new sub 5 max now. – user19547 Aug 15 '16 at 22:29
• @Pandacoder so the run time is varying by a fair bit ~100ms but 2565 seems to average about 5 seconds – user19547 Aug 15 '16 at 22:44
• How long is the number for that? – Pandacoder Aug 15 '16 at 22:45

# Brain-Flak, 54 bytes

([{}]<(())>){(({})()<{({}()<([({})]({}{}))>)}{}{}>)}{}


Try it online!

Multiplication in Brain-Flak takes a long time for large inputs. Just multiplying F100 by F99 with a generic multiplication algorithm would take billions of years.

Fortunately, there's a faster way. A generalized Fibonacci sequence starting with (k, 0) will generate the same terms as the usual sequence, multiplied by k. Using this observation, Brain-Flak can multiply by a Fibonacci number just as easily as it can generate Fibonacci numbers.

If the stack consists of -n followed by two numbers, {({}()<([({})]({}{}))>)}{}{} will computen iterations of the generalized Fibonacci sequence and discard all by the last. The rest of the program just sets up the initial 1 and loops through this for all numbers in the range n...1.

Here's the same algorithm in the other languages provided by this interpreter:

## Brain-Flak Classic, 52 bytes

({}<(())>){(({})[]<{({}[]<(({}<>)<>{}<>)>)}{}{}>)}{}


Try it online!

## Brain-Flueue, 58 bytes

<>(<(())>)<>{(({}<>)<{({}({}))({}[()])}{}>[()]<>)}<>({}){}


Try it online!

## Mini-Flak, 62 bytes

([{}()](())){(({})()({({}()([({})]({}{}))[({})])}{}{})[{}])}{}


Try it online!

# 05AB1E, 6 4 bytes

LÅfP


Try it online!

-1 from Robbie0630, -1 more from an improvement on his suggestion.

• @robbie0630 LÅfP for 4, haven't looked here in a long time ;), you have to actually be careful with € it doesn't work on 2-byte commands. Also, with L, many things vectorize automatically (even list commands) so you don't need an iterator :). – Magic Octopus Urn Feb 20 '18 at 17:14
• Beat me to it :P – Makonede Dec 20 '20 at 19:15

# APL (Dyalog Unicode), 18 bytes

×/(+.!∘⌽⍨∘⍳¨1+∘⍳⊢)


Explanation:

×/(+.!∘⌽⍨∘⍳¨1+∘⍳⊢)
1+∘⍳⊢   ⍝ generate numbers 2-(⍵+1)
¨        ⍝ ... map to each
+.!∘⌽⍨∘⍳         ⍝ n-th fibonacci number
×/                  ⍝ product of all


Fibonacci formula explanation:

+.!∘⌽⍨∘⍳
⍳    ⍝ numbers 1 to ⍵
⍨      ⍝ apply to both sides of +.!∘⌽
⌽       ⍝ reverse the ⍵ vector.
+.!         ⍝ inner product: sum and binomial


Try it online!

• This template may be helpful for future programs. – Razetime Dec 20 '20 at 13:44
• @Razetime I've seen it, but it didn't work for me - I accidentally put my footer code in the footer. I'll use it next time I need to do something – Kamila Szewczyk Dec 20 '20 at 13:47
• Since you're only using the argument once (⊢) and you hand two consecutive atops, a full program would save 3 bytes: ×/+.!∘⌽⍨∘⍳¨1+⍳⎕ – Adám Mar 2 at 15:46

## Mathematica - 32 26 bytes

Fibonacci@i~Product~{i,#}&


@MartinEnder chopped 6 bytes!

## GAP 28 Bytes

Didn't know before today that GAP has a Fibonacci builtin.

n->Product([1..n],Fibonacci)

• Can you link to GAP? No idea what it is. – Leaky Nun Jul 30 '16 at 8:38
• Oh sure (but I'm not the first one to use it here...) – Christian Sievers Jul 30 '16 at 8:44

### Ruby, 85 Bytes

g =->x{(1..x).to_a.collect{|y|(0..y).inject([1,0]){|(a,b),_|[b, a+b]}[0]}.inject(:*)}


Turned out fine, but there's probably a shorter solution.

Fast Fibonnaci calculation taken from here: link

Test it here

# Julia, 36 bytes

!x=[([1 1;1 0]^n)[2]for n=1:x]|>prod


## Clojure, 70 bytes

Clojure isn't really a good language for code golf. Oh well.

Try it at http://tryclj.com.

(last(nth(iterate(fn[[a b r]][b(+ a b)(* r(+ a b))])[0N 1 1])(dec n)))


# Forth, 55 bytes

Uses an iterative approach, built upon my Fibonacci answer in Forth. The results overflow arithmetically for n > 10. The answer is case-insensitive.

: f >r 1 1 r@ 0 DO 2dup + LOOP 2drop 1 r> 0 DO * LOOP ;


Try it online

# Swift, 68 Bytes

func f(n:Int,_ a:Int=1,_ b:Int=1)->Int{return n<1 ?1:a*f(n-1,b,a+b)}