Sum over k of r Choose k by s+k Choose n by -1^r-k

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

Then:


 * $\ds \sum_k \binom r k \binom {s + k} n \paren {-1}^{r - k} = \binom s {n - r}$

where $\dbinom r k$ etc. are binomial coefficients.