Definition:Bernoulli Numbers/Archaic Form/Definition 2

Definition
The old form Bernoulli numbers $B_n^*$ are a sequence of rational numbers defined by the exponential generating function:
 * $\displaystyle 1 - \frac x 2 \cot \frac x 2 = \sum_{n \mathop = 1}^\infty \frac{B_n^* x^{2 n} } {\left({2 n}\right)!}$

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

Also see

 * Equivalence of Definitions of Archaic Form of Bernoulli Numbers