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If (1+x)^n=C0+C1x+C2x^2+.......+Cn x^n ...

If `(1+x)^n=C_0+C_1x+C_2x^2+.......+C_n x^n` , then show that the sum of the products of the coefficients taken two at a time, represented by `sumsum_(0lt=iltjlt=n) ``"^nc_i``"^n c_j` is equal to `2^(2n-1)-((2n)!)/ (2(n !)^2)`

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