Journal of Integer Sequences, Vol. 26 (2023), Article 23.2.6

The (l, r)-Lah Numbers

Aleks Žigon Tankosič
Milojka Štrukelj Elementary School
Delpinova ulica 7
5000 Nova Gorica


After reviewing the definitions and some properties of the Lah numbers and the Stirling numbers of both kinds, as well as their generalizations (r-Lah numbers, r- Stirling numbers of both kinds and (l, r)-Stirling numbers of both kinds), we define the (l, r)-Lah numbers analogously, prove a recurrence relation that they satisfy, express them explicitly as a multiple sum, and present the difference-differential equations satisfied by their column and row generating functions, respectively. Finally, we pose two conjectures, based on experimental evidence.

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(Concerned with sequences A008277 A008297 A132393 A143497 A143498 A143499.)

Received June 27 2022; revised version received January 25 2023. Published in Journal of Integer Sequences, February 25 2023.

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