Mad Binomial Sum

f(n)=m=1nm2(nm) \large f(n) = \sum_{m=1}^n m^2 \dbinom nm

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

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

×

Problem Loading...

Note Loading...

Set Loading...