Sum over k of r-k Choose m by s Choose k-t by -1^k-t

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

Then:


 * $\displaystyle \sum_{k \mathop = 0}^r \binom {r - k} m \binom s {k - t} \paren {-1}^{k - t} = \binom {r - t - s} {r - t - m}$

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