Some combinatorial identities of the r-whitney-eulerian numbers

Toufik Mansour, José L. Ramírez, Mark Shattuck, Sergio N. Villamarín

Research output: Contribution to journalArticlepeer-review


In this paper, we study further properties of a recently introduced generalized Eulerian number, denoted by Am;r(n; k), which reduces to the classical Eulerian number when m = 1 and r = 0. Among our results is a generalization of an earlier symmetric Eulerian number identity of Chung, Graham and Knuth. Using the row generating function for Am;r(n; k) for a fixed n, we introduce the r-Whitney-Euler-Frobenius fractions, which generalize the Euler-Frobenius fractions. Finally, we consider a further four-parameter combinatorial generalization of Am;r(n; k) and find a formula for its exponential generating function in terms of the Lambert-W function.

Original languageEnglish
Pages (from-to)378-398
Number of pages21
JournalApplicable Analysis and Discrete Mathematics
Issue number2
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 University of Belgrade.


  • Combinatorial identity
  • Euler-Frobenius fraction
  • Eulerian number
  • R-Whitney-Eulerian number

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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