# 2014-09 Product of series

For integer $$n \geq 1$$, define
$a_n = \sum_{k=0}^{\infty} \frac{k^n}{k!}, \quad b_n = \sum_{k=0}^{\infty} (-1)^k \frac{k^n}{k!}.$
Prove that $$a_n b_n$$ is an integer.

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