Probability Level 3

$\large f(n) = \sum_{m=1}^n m^2 \dbinom nm$

If the value of $f(2016)$ can be expressed as $A(A+1) 2^B$, where $A$ and $B$ are positive integers, find $A+B$.

Notation: $\dbinom MN$ denotes the binomial coefficient, $\dbinom MN = \dfrac{M!}{N!(M-N)!}$.

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