Given a power sum symmetric polynomial $p_n = an^n/n!$, to show that the generating function $P(t) = ae^x/(1-x)$, for $t = xe^{-x}$

Question

I'm working my way through Macdonald's Symmetric Functions and I have the following question, that I'm having trouble resolving: We're given a power sum symmetric polynomial $$p_n = \frac{an^n}{n!}$$Now I have to show that for $t = xe^{-x}$ the generating function is $$P(t) = \sum p_nt^n = \sum\frac{an^n}{n!}\cdot (xe^{-x})^n = \frac{ae^x}{1-x}$$

Now, the book says to use Lagrange's reversion formula. But I have no idea how to do that. Any kind of hints will be appreciated!