# Sum over partitions

I want to calculate the following sum over non-negative integer partitions $$\sum_{l_1+\cdots +l_n=s} \frac{1}{(l_1!)^2 \cdots (l_n!)^2}.$$ for fixed $n$ and $s.$ I tried to use Vandermonde's identity and induction, but no success so far.

$\ds{\mrm{I}_{\nu}\pars{z}}$ is a Modified Bessel Function.