\begin{definition}[Definition:Bernoulli Numbers/Generating Function]
The '''Bernoulli numbers''' $B_n$ are a sequence of rational numbers defined by the exponential generating function:
:$\ds \frac x {e^x - 1} = \sum_{n \mathop = 0}^\infty \frac {B_n x^n} {n!}$
\end{definition}