# Count stacking sequences [duplicate]

Given a list of stack heights, calculate the number of ways those heights could have been arrived at by stacking blocks one at a time. Shortest code wins.

Test cases:

[2, 2] 6
[3,3,3] 1680
[1,5,9,1] 480480
[] 1
 1
[2,2,2,10] 720720


Reference Python implementation:

def stacking_count(stacks):
if sum(stacks) == 0:
return 1
count = 0
for i, n in enumerate(stacks):
if n == 0:
continue
stacks[i] -= 1
count += stacking_count(stacks)
stacks[i] += 1
return count


# Python 3, 85 bytes

f=lambda a:sum(f(a[:i]+[a[i]-1]+a[i+1:])for i in range(len(a))if a[i])if sum(a)else 1


Try it online!

# Jelly, 6 bytes

;@S!:/


Try it online!

-7 bytes thanks to Jonathan Allan

• ...and hence 6 bytes Mar 2, 2018 at 16:29
• @JonathanAllan oh wait there is a mathematical approach lol Mar 2, 2018 at 16:35
• How about one with only ASCII and what looks almost like a list of emoticons? ;@S!:/ Mar 2, 2018 at 16:40
• @JonathanAllan Ooh cool, sure. Thanks! Mar 2, 2018 at 18:12
• Golfier TIO link as well :P Mar 2, 2018 at 18:12