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A sum with binomial coefficients 2: $\sum_{k=0}^n \frac{1}{k+1} \binom{2k}{k}\binom{2(n-k)+1}{n-k}=\frac{n+1}{n+2}\binom{2n+2}{n+1}$

By ExtraProxies | Proxy Quality | Comments are Closed | 10 December, 2017 | 0

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

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A sum with binomial coefficients 2: $\sum_{k=0}^n \frac{1}{k+1} \binom{2k}{k}\binom{2(n-k)+1}{n-k}=\frac{n+1}{n+2}\binom{2n+2}{n+1}$

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