Are you crazy? It's 2016

Probability Level 4

r=12016r3(2016r)\large{\begin{aligned}\sum_{r=1}^{2016} r^3\binom{2016}{r} \end{aligned}}

If the value of the summation above is equal to AA, find the sum of digits of the number A2016×22016 \dfrac A{2016\times 2^{2016}} when it is written in decimal representation.

(This problem is not original)

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