Factors of each term of a Polynomial Power

%By Chukwunomso Agunwamba
%In order to form the new terms in the new polynomial, it calculates the  
%powers to which one should raise the coefficients of a polynomial, when the
%the polynomial of opw number of terms is raised to a power of n.  
 
##This mathematical code is provided as is, for the end user to be able to use  
##it and to edit it for educational purposes. However, any modified version must  
##include my name as the original producer of the code.
 
##The name of the mfile code is getcoeffnthpw. It has two required input  
##arguments and an optional third input argument.  
##The first input is the power to raise the polynomial to.   
##The second input is the number of terms in the original polynomial, which is  
##the length of the vector of coefficients.  
##The optional third argument is the coefficient vector of the polynomial  
##you want to multiply n times.
 
 
##So, symbolically speaking (not strictly usage syntax),  
##P^n = P.^getcoeffnthpw(n,opw) is the desired usage. For example,  
#[3 2].^getcoeffnthpw(3,2) gives
##ans =
##
##   27    1
##    9    2
##    3    4
##    1    8
##(I was using the implied first output variable, ignoring the 2nd output.)
 
##So care must be taken to get the intended result, as the 1s that appear beside
##27 and beside 8 are a result of zero filling the empty locations of the  
##matrix, not the actual powers for 2 or for 3 respectively. That is the desired
##list of powers should be of the form:
##
##    27 empty
##    9          2
##    3          4
##    empty 8
## Here, 'empty's can be replaced with zeros.
 
##Usage syntax example:
##[h, coefficients] = getcoeffnthpw(n,opw);
##
##n = 3
##P = [3 2 5]
##opw = length(P)
##h = getcoeffnthpw(n,opw)
##G = (P.^h)
##G is the desired result that has the factors of each new coefficient
##explained out before that new coefficient is finally calculated.
##G =
##
##    27     1     1
##     9     2     1
##     9      1     5
##     3     4     1
##     3     2     5
##     3      1   25
##     1      8     1
##     1      4     5
##     1      2   25
##     1      1   125
##
##To get the final coefficient vector, one can place h into the multichoose
##function to account for how many times each term occurs after the product.
 
##Example with multichoose:
##coefficients = (prod(G.').').*multichoose(h)
 
##feel free to change or remove/disable the default inputs