Generalized poly-Cauchy and poly-Bernoulli numbers by using incomplete \(r\)-Stirling numbers

DOI10.1007/s00010-017-0509-4zbMath1422.11046OpenAlexW2763225741MaRDI QIDQ1689414

José L. Ramírez, Takao Komatsu

Publication date: 12 January 2018

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-017-0509-4

zbMATH Keywords

combinatorial identitiesgenerating functionpoly-Bernoulli numberspoly-Cauchy numbersincomplete \(r\)-Stirling numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Combinatorial identities, bijective combinatorics (05A19) Bernoulli and Euler numbers and polynomials (11B68)

Related Items (4)

On \(q\)-poly-Bernoulli numbers arising from combinatorial interpretations ⋮ Extensions of set partitions and permutations ⋮ A \((p, q)\)-analog of poly-Euler polynomials and some related polynomials ⋮ Restricted \(r\)-Stirling numbers and their combinatorial applications

Cites Work

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• Poly-Cauchy numbers with a \(q\) parameter
• Generalized Bessel numbers and some combinatorial settings
• Real zeros and partitions without singleton blocks
• The \(r\)-Stirling numbers
• Involutions and their progenies
• \(q\)-poly-Bernoulli numbers and \(q\)-poly-Cauchy numbers with a parameter by Jackson's integrals
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• Poly-Bernoulli numbers
• Combinatorial and arithmetical properties of the restricted and associated Bell and factorial numbers
• Incomplete poly-Bernoulli numbers and incomplete poly-Cauchy numbers associated to the \(q\)-Hurwitz-Lerch zeta function
• On the unimodality and combinatorics of Bessel numbers
• Incomplete Cauchy numbers
• Poly-Bernoulli numbers and polynomials with a \(q\) parameter
• Reciprocity for multirestricted Stirling numbers
• The Cauchy numbers
• POLY-CAUCHY NUMBERS
• POLYLOGARITHMS AND POLY-BERNOULLI POLYNOMIALS
• Combinatorics of Set Partitions
• Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers
• Periodicity of the last digits of some combinatorial sequences
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