Definition:Euler Numbers

Definition
The Euler Numbers $E_n$ are a sequence of integers defined by the exponential generating function:


 * $\displaystyle \operatorname {sech} x = \frac {2 e^x} {e^{2 x} + 1} = \sum_{n \mathop = 0}^\infty \frac {E_n x^n} {n!}$

where $\left\lvert{x}\right\rvert < \dfrac \pi 2$.

Also known as
The Euler numbers are also known as the secant numbers or zig numbers.