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
numbers of both kinds), we define the (l, r)-Lah numbers analogously,
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.
Full version: pdf,
(Concerned with sequences
Received June 27 2022; revised version received January 25 2023.
Published in Journal of Integer Sequences,
February 25 2023.
Journal of Integer Sequences home page