  We prove that for any nonnegative integers $n$ and $r$ the binomial sum $$
\sum_{k=-n}^n\binom{2n}{n-k}k^{2r} $$ is divisible by
$2^{2n-\min\{\alpha(n),\alpha(r)\}}$, where $\alpha(n)$ denotes the number of
1's in the binary expansion of $n$. This confirms a recent conjecture of Guo
and Zeng.
