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Question Number 22739 by Tinkutara last updated on 22/Oct/17

I f {(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} + C_{3} x^{3}

+ \dots + C_{n} x^{n},

P r o v e t h a t \underset{0 ⩽ i < j ⩽ n}{Σ Σ} (i + j) C_{i} C_{j} =

n (2^{2 n - 1} - \frac{1}{2}^{2 n} C_{n})