The translated Whitney–Lah numbers: generalizations and q-analogues

Mahid M. Mangontarum
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 4, Pages 80–92
DOI: 10.7546/nntdm.2020.26.4.80-92
Full paper (PDF, 203 Kb)

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Authors and affiliations

Mahid M. Mangontarum
Department of Mathematics, Mindanao State University–Main Campus
Marawi City 9700, Philippines

Abstract

In this paper, we derive some combinatorial formulas for the translated Whitney–Lah numbers which are found to be generalizations of already-existing identities of the classical Lah numbers, including the well-known Qi’s formula. Moreover, we obtain q-analogues of the said formulas and identities by establishing similar properties for the translated q-Whitney numbers.

Keywords

• Lah numbers
• translated Whitney–Lah numbers
• Qi’s formula
• q-analogues.

2010 Mathematics Subject Classification

• 05A19
• 05A30
• 11B65

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