\frac{1}{e^x-x-1}=\frac{1}{\frac{x^2}{2}(1+\frac{2x}{3!}+\frac{2x^2}{4!}+...)}=\frac{2}{x^2}\frac{1}{1+\frac{2x}{3!}+\frac{2x^2}{4!}+...}