Efficient Matlab implementation of Multinomial Coefficient

Question

I want to calculate the multinomial coefficient:

where it is satisifed

Answer 1

Another approach is to use Yannis Manolopoulos iterative method. Suppose we have a vector k with the multinomial entries.

function N = multicoeff (k),
  n=sum(k); 
  [_,imax]=max(k); 
  num=[n:-1:n-k(imax)-1]; 
  den=[]; k(imax)=[]; 
  for i=1:length(k), den=[den 1:k(i)]; endfor; 
  N=prod(num./den);
endfunction

example

octave:2> k = [5 4 3];
octave:3> multicoeff (k)
ans =  27720

Reference: Yannis Manolopoulos. Binomial coefficient computation. ACM SIGCSE Bulletin, 34(4):65, December 2002. doi: 10.1145/820127.820168. URL https: //doi.org/10.1145/820127.820168.