Powers of 2 and the binomial expansion

Discrete Mathematics 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.