f(x) = (\frac{x}{1!}+\frac{x^2}{2!}+\cdots)(\frac{1}{0!}+\frac{x}{1!}+\frac{x^2}{2!})(\frac{1}{0!}+\frac{x}{1!}+\frac{x^2}{2!}+\cdots)^2 = e^{2x}(e^x - 1)(1+x+\frac{x^2}{2})