Powers of 2 and the binomial expansion

Probability Level 4

$1^2 \binom{2017}{1} + 2^2 \binom{2017}{2} + 3^2 \binom{2017}{3} + \cdots + 2017^2 \binom{2017}{2017}$

Find the maximum value of integer $n$ such that $2^n$ divides the expression above.