Definition:Bernoulli Numbers/Archaic Form

Definition
Some sources define the Bernoulli numbers ${B_n}^*$ to be a sequence of rational numbers defined by the exponential generating function:


 * $\displaystyle \frac x {e^x - 1} = 1 - \frac x 2 + \sum_{n \mathop = 1}^\infty \left({-1}\right)^{n - 1} \frac{ {B_n}^* x^{2 n} } {\left({2 n}\right)!}$

Under this convention, the values of the first Bernoulli numbers are:

However, this definition is generally considered archaic, and will not be used on.