Simplication

Algebra Level 4

$\large \sum_{n=1}^{2016} (-1)^n \dfrac{n^2+n+1}{n!}$

If the summation above can be expressed as $$-a + \dfrac b{c!}$$, where $$a,b$$ and $$c$$ are integers, find $$a-b+c$$.

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