If we have the sum of two binomial coefficients,
$$\sum_{k=0}^{r}\binom m k\binom{ n-m}{ r-k} = \binom n r$$
We can use vandermonde's identity to prove this. The result is the familiar hypergeometric distribution.
Now, what I was wondering is if this formula:
$$\sum_{m=0}^{n}\binom m k\binom{ n-m}{ r-k}$$
has some general solution.
