Definition:Bernoulli Numbers/Archaic Form/Definition 1

Definition
The old form Bernoulli numbers ${B_n}^*$ are a sequence of rational numbers defined by the exponential generating function:

for $x \in \R$ such that $\left\lvert{x}\right\rvert < 2 \pi$

Also see

 * Equivalence of Definitions of Archaic Form of Bernoulli Numbers