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I am struggling to verify this identity. I've tried using the Principle of Mathematical Induction, combinatorial proofs, and a generalization of Vandermonde's Identity, all to no avail. It's the $(2n)!$ that's giving me problems.

Pedro
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Stephen Steward
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  • I strongly advise you to look at this link http://math.stackexchange.com/questions/983815/vandermond-identity-corollary-sum-v-0n-frac2nv2n-v2-2n-c?rq=1 – Khadija Mbarki Feb 14 '16 at 23:15

1 Answers1

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Hint for a direct proof:

Calculate the coefficient of $x^n$ in $(1+x)^{2n}$ and compare with the coefficient of $x^n$ in $(1+x)^n(1+x)^n$.

Bernard
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