relation between 2 series

Question

imagine we get $ f(x)= \sum_{n=0}^{\infty}a(n)x^{n} $

and $ g(x)= \sum_{n=0}^{\infty}\frac{a(n)}{n!}x^{n} $

then if i know $ g(x)$ i can get $ f(x) $ using laplace transform but what if i know only the value of $ f(x) $ ??