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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}12(12017)+22(22017)+32(32017)+⋯+20172(20172017)
Find the maximum value of integer nnn such that 2n2^n2n divides the expression above.
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