\begin{definition}[Definition:Euler Numbers]
The '''Euler Numbers''' $E_n$ are a sequence of integers defined by the exponential generating function:
:$\ds \sech x = \frac {2 e^x} {e^{2 x} + 1} = \sum_{n \mathop = 0}^\infty \frac {E_n x^n} {n!}$
where $\size x < \dfrac \pi 2$.
\end{definition}