KöMaL 2023 B5348

Let $b$, $c$ and $n$ be non-negative integers satisfying $0\le c\le b-2n$. Prove that $\sum_{a=0}^n \binom{2a}{a}\binom{b-2a}{n-a} = \sum_{a=0}^n \binom{2a+c}{a}\binom{b-c-2a}{n-a}.$