Powers of 2 and the binomial expansion

Probability Level 3

12(20171)+22(20172)+32(20173)++20172(20172017)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 nn such that 2n2^n divides the expression above.

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