Multinomial coefficient

[salvomic]

ok,
after some tries, I simplified all with this:

Code:


EXPORT Multinomial()
BEGIN
local n,k;
input ({n, {k}}, "Multinomial Coefficient", {"n", "k_i list"}, {"Total n", "input {k_i list} with comma"}, {0,0});
// we need integers (also for list)
n:=IP(n); k:=IP(k);

return n!/∏List(k!);
END;

This program accept an integer for "n" and a list with {} for the list of k (like {1,4,4,2}) and give a integer that represent permutations in a multi set...

There are some (ugly) problems:
1. a way to avoid user to input also the {} for the list (it would better to have only something like 1,4,4,2)
2. a control because the sum of k must be equal to n

Any hints are welcome!