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Prove $$\sum_{k=0}^n\binom nk\binom{m+k}n=\sum_{k=0}^n\binom nk\binom{m}k2^k$$

I know LHS is the number of ways to divide group of $m+k$ people to three groups of $k,n-k,m+k-n$ people each but since the interative is also involved it doesnt feel right.

Algebraic solutions are also welcome

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marked as duplicate by Robert Z, Community Jun 8 '18 at 14:37

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  • $\begingroup$ Can someone tell me how to even find these. How to type the binomial notation in search box? $\endgroup$ – Anvit Jun 8 '18 at 14:38

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