Geodesic
A generalization of Stirling numbers of the second kind via a special multiset
Journal of integer sequences, Tome 13 (2010) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 05A15, 05A18, 11B37, 11B73
Keywords: Stirling numbers of the second kind, Bell numbers, generating functions, multisets, partitions, recurrence relations 
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     author = {Griffiths, Martin and Mez\H{o}, Istv\'an},
     title = {A generalization of {Stirling} numbers of the second kind via a special multiset},
     journal = {Journal of integer sequences},
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     year = {2010},
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Griffiths, Martin; Mező, István. A generalization of Stirling numbers of the second kind via a special multiset. Journal of integer sequences, Tome 13 (2010) no. 2. http://geodesic.mathdoc.fr/item/JIS_2010__13_2_a5/