Geodesic
The $r$-Bell numbers
Journal of integer sequences, Tome 14 (2011) no. 1.

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

Summary: 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.
Classification : 05A18, 05A15
Keywords: Bell numbers, r-Bell numbers, Stirling numbers, r-Stirling numbers, Hankel determinants, restricted partitions 
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     author = {Mez\H{o}, Istv\'an},
     title = {The $r${-Bell} numbers},
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     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_1_a2/}
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Mező, István. The $r$-Bell numbers. Journal of integer sequences, Tome 14 (2011) no. 1. http://geodesic.mathdoc.fr/item/JIS_2011__14_1_a2/