The r-Bell Numbers
Department of Applied Mathematics and Probability Theory
Faculty of Informatics
University of Debrecen
P. O. Box 12
The notion of r-Stirling numbers implies the
definition of generalized Bell (or r-Bell) numbers. The r-Bell
numbers have appeared in several works, but there is no systematic treatise
on this topic. In this paper we fill this gap. We discuss the most
important combinatorial, algebraic and analytic properties of these
numbers, which generalize similar properties of the Bell numbers. Most
of these results seem to be new. It turns out that in a paper of
Whitehead, these numbers appeared in a very different context. In
addition, we study the so-called r-Bell polynomials.
Full version: pdf,
(Concerned with sequences
Received November 1 2010;
revised version received December 19 2010.
Published in Journal of Integer Sequences, December 19 2010.
Journal of Integer Sequences home page