Recurrence relations of poly-Cauchy numbers by the $r$-Stirling transform

Abstract

We give some formulas of poly-Cauchy numbers by the $r$-Stirling transform. In the case of the classical or poly-Bernoulli numbers, the formulas are with Stirling numbers of the first kind. In our case of the classical or poly-Cauchy numbers, the formulas are with Stirling numbers of the second kind. We also discuss annihilation formulas for poly-Cauchy number with negative indices.

Mediterr. J. Math.(2022)

References in corpus (3)

• Polynomials with r-Lah coefficient and hyperharmonic numbers
• Extended Bernoulli and Stirling matrices and related combinatorial identities
• New identities with Stirling, hyperharmonic, and derangement numbers, Bernoulli and Euler polynomials, powers, and factorials

Cited by in corpus (1)

• Poly-Cauchy numbers -- the combinatorics behind