solving power series expression? Can anyone show how to simplify $$\frac{\sum_{n=1}^\infty n\frac{n^{n-1}}{n!}x^{n-1}}{(-1+\sum_{n=1}^\infty \frac{n^{n-1}}{n!}x^n)^2}$$


Hint: The Lambert W function admits the expansion
  \begin{align*}
\sum_{n=1}^\infty n^{n-1}\frac{x^n}{n!}=-W(-x)\qquad\qquad |x|<\frac{1}{e}
\end{align*}

