Any ideas to show the following identity : $ \forall n \in \mathbb{N},\ \sum_{k=0}^n \frac{1}{k+1} \binom{2k}{k}\binom{2(n-k)+1}{n-k}=\frac{n+1}{n+2}\binom{2n+2}{n+1}$ Thanks a lot for your helpRead more
Any ideas to show the following identity : $ \forall n \in \mathbb{N},\ \sum_{k=0}^n \frac{1}{k+1} \binom{2k}{k}\binom{2(n-k)+1}{n-k}=\frac{n+1}{n+2}\binom{2n+2}{n+1}$ Thanks a lot for your helpRead more