Journal of Integer Sequences, Vol. 12 (2009), Article 09.5.7

Generalized Near-Bell Numbers

Martin Griffiths
Department of Mathematical Sciences
University of Essex
Wivenhoe Park
United Kingdom


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 general multisets.

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(Concerned with sequences A000110 and A035098.)

Received April 27 2009; revised version received July 14 2009. Published in Journal of Integer Sequences, July 16 2009.

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