Sum over k of r Choose m+k by s Choose n+k

Theorem
Let $s \in \R, r \in \Z_{\ge 0}, m, n \in \Z$.

Then:
 * $\displaystyle \sum_k \binom r {m + k} \binom s {n + k} = \binom {r + s} {r - m + n}$

where $\dbinom r {m + k}$ etc. are binomial coefficients.