The well-known Vandermonde convolution gives us the closed form $\sum_{k=0}^n {r\choose k}{s\choose n-k} = {r+s \choose n}$. For the case $r=s$, it is also known that $\sum_{k=0}^n (-1)^k {r \choose k} {r \choose n-k} = (-1)^{n/2} {r \choose n/2} [n \mathrm{\ is\ even}]$.
When $r\not= s$, is there a known closed form for the alternating Vandermonde sum $\sum_{k=0}^n (-1)^k {r \choose k} {s \choose n-k}$?