$n(n+1)2^{n-2} = \sum_{i=1}^ni^2\binom{n}{i}$
I would like to prove above identity combinatorially.
$n(n+1)$ of LHS is doubled amount of summing up from $1$ to $n$ and remaining $2^{n-1}$ denotes that there's some $n -1$ consecutive choice of something being exist or not.
How could I relate this two factors into potential those of RHS ?
Or will there any other option that I can refer to?
Any advice would be appreciate.