I am finding some trouble in calculating the following sum involving the hypergeometric function, power and factorial functions. 
$$
\sum\_{y=1}^\infty \mathrm{e}^z \cdot {}\_1F\_1\left(1-y;2;-z\right) \frac{\mu^y}{y!} \mathrm{e}^{-\mu} 
$$

Could you please provide me some hints to solve this sum?
Thank you in advance