Monotonic Exponential Generating Functions

SUPERSPECIES

$\displaystyle \dfrac{x}{1-e^{-x}} = \sum_{n \geq 0} (-1)^n\,B_n^{-}\,\dfrac{x^n}{n!} \\ = 1 + \dfrac{1}{2}\,x + \dfrac{1}{6}\,\dfrac{x^2}{2!} + \dfrac{1}{30}\,\dfrac{x^4}{4!} + \dfrac{1}{42}\,\dfrac{x^6}{6!} + \cdots$

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