Journal of Integer Sequences, Vol. 23 (2020), Article 20.5.2

A (p, q)-Deformed Recurrence for the Bell Numbers

Lahcen Oussi
Institute of Mathematics University of Wrocaw
Pl. Grunwaldzki 2/4
50-384 Wrocaw


We obtain a (p, q)-deformation of the recurrence formula for the Bell numbers, using algebraic techniques. Specializing to the case p = 1 and the case p = q = 1, respectively, we recover the generalized recurrence formula for Bell numbers as obtained by Katriel and Spivey, in related papers.

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(Concerned with sequences A000110 A008277.)

Received December 4 2019; revised versions received December 13 2019; February 7 2020; March 25 2020; May 4 2020; May 6 2020. Published in Journal of Integer Sequences, May 7 2020.

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