Can anyone show how to simplify $$\frac{\sum_{n=1}^\infty n\frac{n^{n-1}}{n!}x^{n-1}}{(-1+\sum_{n=1}^\infty \frac{n^{n-1}}{n!}x^n)^2}$$
Answer
small hint
the derivative of $$\frac{1}{1-f}$$ is
$$\frac{f'}{(-1+f)^2}.$$
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