Definition:Bernoulli Numbers

Definition
The Bernoulli numbers $B_n$ are a sequence of rational numbers defined by the Exponential Generating Function:


 * $\displaystyle \frac x {e^x - 1} = \sum_{n \mathop = 0}^\infty \frac{B_n x^n} {n!}$

The values of the first Bernoulli Numbers are:


 * $1, - \dfrac 1 2, \dfrac 1 6, 0, - \dfrac 1 {30}, 0, \dfrac 1 {42}, 0, - \dfrac 1 {30} \ldots$

This numerators and denominators are listed in A027641 and A027642 respectively.