Is there a closed-form solution to the following sum? \begin{align*} f(r, s, n) = \sum_{k=0}^{n}c^k\binom{r}{k}\binom{s}{n-k} \end{align*} I know this corresponds to find the coefficient of $x^n$ of the generating function \begin{align*} (1+cx)^r(1+x)^s \end{align*} but I don't know how to proceed from here. Any inputs would be great!
2026-04-09 03:49:41.1775706581
Vandermonde-type convolution with geometric term
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