Yet Another Ode To 2016

Probability Level 4

The value of k=0672(20163k)\displaystyle\sum_{k=0}^{672} \dbinom{2016}{3k} can be expressed in the form ab+cd\dfrac{a^{b} + c}{d} where a,ca,c and dd are prime. Find a+b+c+da + b + c + d.

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