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Prove that (""^(2n)C(0))^3-(""^(2n)C(1))...

Prove that `(""^(2n)C_(0))^3-(""^(2n)C_(1))^3-(""^(2n)C_(2))^3-.....+(-1)^n(""^(2n)C_(2n))^2=(-1)^n.""^(2n)C_(n)`

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