\newcommand{\combination}[2]{ \left( \begin{array}{c} #1 \\ #2 \end{array} \right ) }
\newcommand{\largesum}[2]{ \begin{array}{c} \scriptstyle{#2} \\ \sum \\ \scriptstyle{#1} \end{array} }
~ ... ~ = \largesum{k=0}{\infty}\frac{1}{k!} \largesum{r=0}{k} (-1)^{k-r} \combination{k}{r} r^n 
= \largesum{r=0}{\infty} \frac{r^n}{r!} \largesum{k=r}{\infty} \frac{(-1)^{k-r}}{(k-r)!} = \frac{1}{e} \largesum{r=0}{\infty} \frac{r^n}{r!}