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