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

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

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