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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