Still a Messy Close Form?

Algebra Level 4

n=12015[(1)n(n2+n+1n!)] \large \sum_{n=1}^{2015} \left [ (-1)^n \left ( \frac { n^2+n+1}{n!} \right ) \right ]

If the summation equals to abc! -a - \frac {b}{c!} for positive integers a,b,ca,b,c

What is the minimum value of a+b+ca+b+c?

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