If I have a generating function for $f(n)$ defined by
$g(x)=\displaystyle\sum_{n=0}^{\infty}f(n)x^n=\dfrac{P(x)}{Q(x)}$,
where $P(x)$ and $Q(x)$ are polynomials and $Q(x)$ is not the zero function, how could I show that $f(n)$ is not more than exponential?