Composite Maclaurin Series Coefficient

The function $f$ has a Maclaurin series given by $x + \displaystyle\frac{1}{2}x^2 + \displaystyle\frac{1}{6}x^3 + \displaystyle\frac{1}{24}x^4 + \cdots$, which converges to $f(x)$ for all real numbers $x$. If $g(x) = e^{-f(x)}$, what is the coefficient of the $x^3$ term in the Maclaurin series for $g$?