Determine, with proof, the closed form of following expression in terms of n

Σ_{j=1 to n}  j²*(j+1)*(ⁿC_j)

Charlie, (2(n+1)^3-(n+1)^2+5n^2-1)*2^n/16 (equivalently,(n^3+5n^2+2n)*2^n/8)  solves for all n in your list.

Does this count as 'proof'?

Edited on April 29, 2011, 7:25 am

Posted by broll on 2011-04-29 06:32:58