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?
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