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$\large a_{n+2} = (n + 3)a_{n+1} - (n + 2)a_{n}$

For whole numbers $n$, consider the recurrence relation defined as above with $a_{1} = 1, a_{2} = 3$.

Find $\displaystyle\bigg( \sum_{k=1}^{2015} a_{k} \bigg)\pmod{100}.$

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