How can I understand this identity on an example?
$\sum_{k=1}^n k^2{n \choose k} = n(n+1)2^{n-2}$
For the left side it could be like I am choosing k people from n for each k > 0 and then 2 people from the k chosen people with chosing the same person twice allowed and order matters, only when k = 1 order does not matter. How can I say it similarly with the right side?