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Prove that (1^2)/3""^n C1+(1^2+2^2)/5^n ...

Prove that `(1^2)/3""^n C_1+(1^2+2^2)/5^n C_2 + (1^1+2^2+3^2)/7^n C_3+` `+(1^2+2^2++n^2)/(2n+1)^n C_n=(n(n+3))/6 *2^(n-2)dot`

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