How to compute an iterated product in Sage
I am wondering about how to define a function f(n, k, i)
that will take inputs n
, k
, i
and give me the following product:
\prod_{\ell = 1}^i {n + k - \ell \choose k}
So for i = 2, this would look like {n + k - 1 \choose k}\cdot {n + k - 2 \choose k}. Would I use a for loop to iteratively add to the product until all i
terms were accounted for?