Generalized Near-Bell Numbers
Department of Mathematical Sciences
University of Essex
The $n$th near-Bell number, as defined by Beck, enumerates all possible
partitions of an n-multiset with multiplicities 1,1,1,...,1,2.
In this paper we study the sequences arising from a generalization of
the near-Bell numbers, and provide a method for obtaining both their
exponential and their ordinary generating functions. We derive various
interesting relationships amongst both the generating functions and the
sequences, and then show how to extend these results to deal with more
Full version: pdf,
(Concerned with sequences
Received April 27 2009;
revised version received July 14 2009.
Published in Journal of Integer Sequences, July 16 2009.
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