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Zbl 1221.11061
Wang, Weiping
Generalized higher order Bernoulli number pairs and generalized Stirling number pairs.
(English)
[J] J. Math. Anal. Appl. 364, No. 1, 255-274 (2010). ISSN 0022-247X

Given a formal power series $f(t)=\sum_{k=1}^{\infty}f_{k}\frac{t^{k}}{k!}$ and its compositional inverse $g(t)=\sum_{k=1}^{\infty }g_{k}\frac{t^{k}}{k!}$, the higher order Bernoulli numbers of the first and second kind associated with the series $f(t)$ are defined, some explicit expressions and recurrence relations are given, and plenty of relations including Stirling numbers are derived.
[Mehmet Cenkci (Antalya)]
MSC 2000:
*11B68 Bernoulli numbers, etc.
11B73 Bell and Stirling numbers
05A19 Combinatorial identities

Keywords: Generalized higher order Bernoulli numbers; generalized Stirling numbers; delta series; combinatorial identities

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