A recurrence to relate to

Algebra Level 5

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

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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