I'm wondering if a closed form expression, not involving the hypergeometric function, exists for the following sum
$$ \sum_{k=0}^{n}\binom{n}{k}\binom{q-k}{r} $$
where $q \geq n$, and $n,k,q,r$ are all non-negative integers, and $\binom{0}{r}=1$ if $r$ is $0$, and $0$ otherwise. It's not amenable to a Vandermonde convolution due to $k$ appearing in both the upper and lower indices, and upper negation has not proved useful. I could not find any related identities in Concrete Mathematics or in Henry W. Gould's collected identities involving binomial coefficients. If no closed form exists this information will also be valuable to me. Any hints or suggestions are greatly appreciated.