I would like to prove the following statement to be true. $$ \sum_{k = 0}^{m} \binom{m}{k}\binom{n+k}{m} = \sum_{k = 0}^{m}\binom{n}{k}\binom{m}{k}2^{k} $$


marked as duplicate by Namaste, Jendrik Stelzner, N. F. Taussig combinatorics Aug 26 '18 at 11:16

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  • $\begingroup$ First, I would try to express the combinatorial expressions as fractions. $\endgroup$ – David Aug 26 '18 at 11:08