Sum over k of r-tk Choose k by s-t(n-k) Choose n-k by r over r-tk

Theorem
Let $r, s, t \in \R, n \in \Z$.

Then:


 * $\ds \sum_{k \mathop \ge 0} \binom {r - t k} k \binom {s - t \paren {n - k} } {n - k} \frac r {r - t k} = \binom {r + s - t n} n$

where $\dbinom {r - t k} k$ and so on are binomial coefficients.