Geodesic
The \(r\)-Bell numbers
Journal of integer sequences, Tome 14 (2011) no. 1
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 
@article{JIS_2011__14_1_a2,
     author = {Mez\H{o},  Istv\'an},
     title = {The {\(r\)-Bell} numbers},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {1},
     zbl = {1205.05017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_1_a2/}
}
TY  - JOUR
AU  - Mező,  István
TI  - The \(r\)-Bell numbers
JO  - Journal of integer sequences
PY  - 2011
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JIS_2011__14_1_a2/
LA  - en
ID  - JIS_2011__14_1_a2
ER  - 
%0 Journal Article
%A Mező,  István
%T The \(r\)-Bell numbers
%J Journal of integer sequences
%D 2011
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/JIS_2011__14_1_a2/
%G en
%F JIS_2011__14_1_a2
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/