The r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers

Authors

  • Roberto Bagsarsa Corcino Cebu Normal University https://orcid.org/0000-0003-1681-1804
  • Charles Montero Mindanao State University-Marawi Campus
  • Maribeth Montero Mindanao State University-Marawi Campus
  • Jay Ontolan Cebu Normal University

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i3.3494

Keywords:

$r$-Dowling numbers, $(r, \beta)$-Bell numbers, Bell polynomials, Lah numbers, $r$-Whitney numbers, Faa di Bruno's formula, $r$-Whitney-Lah numbers

Abstract

This paper derives another form of explicit formula for $(r,\beta)$-Bell numbers using the Faa di Bruno's formula and certain identity of Bell polynomials of the second kind. This formula is expressed in terms  of the $r$-Whitney numbers of the second kind and the ordinary Lah numbers. As a consequence, a relation between $(r,\beta)$-Bell numbers and the sums of row entries of the product of two matrices containing the $r$-Whitney numbers of the second kind and the ordinary Lah numbers is established.  Moreover, a $q$-analogue of the explicit formula is obtained.

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How to Cite

Corcino, R. B., Montero, C., Montero, M., & Ontolan, J. (2019). The r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers. European Journal of Pure and Applied Mathematics, 12(3), 1122–1137. https://doi.org/10.29020/nybg.ejpam.v12i3.3494

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