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Prove that (""^(2n)C(0))^(2)-(""^(2n)C(1...

Prove that `(""^(2n)C_(0))^(2)-(""^(2n)C_(1))^(2)+(""^(2n)C_(2))^(2)-…+(""^(2n)C_(2n))^(2)=(-1)^(n)*""^(2n)C_(n)`.

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