# [05AB1E], <s>10</s> 9 bytes

-1 byte thanks to [Erik the Outgolfer](https://codegolf.stackexchange.com/users/41024/erik-the-outgolfer)

    sF³gݨm*O

[Try it online!][TIO-j5xtm7k5]

Takes x as first argument, n as second and p in ascending order as third.

###Explanation###
    sF³gݨm*O
    s         # Forces the top two input arguments to get pushed and swaped on the stack
     F        # Do n times...
      ³        # Push the third input (the coefficients)
       g       # Get the length of that array...
        ݨ     # and create the range [0 ... length]
          m    # Take the result of the last iteration to these powers (it's just x for the first iteration)
           *   # Multiply the resuling array with the corresponding coefficients
             O # Sum the contents of the array
              # Implicit print
[05AB1E]: https://github.com/Adriandmen/05AB1E
[TIO-j5xtm7k5]: https://tio.run/##MzBNTDJM/f@/2O3Q5vTDcw@tyNXy///fSM@Yy4QrWtdERxfI1DHQM4wFAA "05AB1E – Try It Online"