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:


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

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


 * $\dfrac 1 6, \dfrac 1 {30}, \dfrac 1 {42}, \dfrac 1 {30}, \dfrac 5 {66}, \dfrac {691} {2730}, \ldots$