A recurrence to relate to

Algebra Level 3

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

For whole numbers nn, consider the recurrence relation defined as above with a1=1,a2=3a_{1} = 1, a_{2} = 3.

Find (k=12015ak)(mod100).\displaystyle\bigg( \sum_{k=1}^{2015} a_{k} \bigg)\pmod{100}.

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