Journal of Integer Sequences, Vol. 13 (2010), Article 10.2.5

A Generalization of Stirling Numbers of the Second Kind via a Special Multiset

Martin Griffiths
School of Education (Mathematics)
University of Manchester
Manchester M13 9PL
United Kingdom

István Mező
Department of Applied Mathematics and Probability Theory
Faculty of Informatics
University of Debrecen
H-4010 Debrecen
P. O. Box 12


Stirling numbers of the second kind and Bell numbers are intimately linked through the roles they play in enumerating partitions of n-sets. In a previous article we studied a generalization of the Bell numbers that arose on analyzing partitions of a special multiset. It is only natural, therefore, next to examine the corresponding situation for Stirling numbers of the second kind. In this paper we derive generating functions, formulae and interesting properties of these numbers.

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(Concerned with sequences A000110 A000392 A000453 A000670 A008277 A008284 A019538 A035098 A083329 A168583 A168584 A168585 A168604 A168605 A168606 A169587 A169588 A172106 A172107 A172108 A172109 A172110 A172111.)

Received August 7 2009; revised versions received October 8 2009; January 31 2010. Published in Journal of Integer Sequences, January 31 2010.

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