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

Theorem
Let $m, n \in \Z_{\ge 0}$.

Then:


 * $\ds \sum_{k \mathop \in \Z} \binom {m - r + s} k \binom {n + r - s} {n - k} \binom {r + k} {m + n} = \binom r m \binom s n$

Also see

 * Dixon's Identity/General Case