Coefficient of a Composite Maclaurin Series

Let the function $f$ have a Maclaurin series $1 + 2x + \displaystyle\frac{1}{2}x^2 + \displaystyle\frac{1}{6}x^3 + \cdots$ that converges to $f(x)$ for all real numbers $x$. If $g(x) = e^{f(x)}$, what is the coefficient of $x^3$ in the Maclaurin series for $g$?