Double summation for this series

$$
\sum_{n=0}^{\infty}\left(\frac{x^n}{n!}\sum_{r=0}^{n-1}\left(\frac{y^r}{r!}\right)\right)
$$

This is a double summation I need to evaluate(not for a homework problem, but for a probability question involving gaming I found). I can't find any idea how to do this and wolfram alpha can't calculate this with extended computer time either, though this series is obviously less than e^(x+y) and monotonous, so it converges.