Geodesic
Extended Bell and Stirling numbers from hypergeometric exponentiation
Journal of integer sequences, Tome 4 (2001) no. 1.

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

Summary: Exponentiating the hypergeometric series $_{0}F_{L}$(1,1,$\dots $,1;z), L = 0,1,2,$\dots $, furnishes a recursion relation for the members of certain integer sequences $b_{L}(n)$, n = 0,1,2,$\dots $. For L >= 0, the $b_{L}(n)$'s are generalizations of the conventional Bell numbers, $b_{0}(n)$. The corresponding associated Stirling numbers of the second kind are also investigated. For L = 1 one can give a combinatorial interpretation of the numbers $b_{1}(n)$ and of some Stirling numbers associated with them. We also consider the L>1 analogues of Bell numbers for restricted partitions. 
@article{JIS_2001__4_1_a3,
     author = {Sixdeniers, J.-M. and Penson, K.A. and Solomon, A.I.},
     title = {Extended {Bell} and {Stirling} numbers from hypergeometric exponentiation},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2001__4_1_a3/}
}
TY  - JOUR
AU  - Sixdeniers, J.-M.
AU  - Penson, K.A.
AU  - Solomon, A.I.
TI  - Extended Bell and Stirling numbers from hypergeometric exponentiation
JO  - Journal of integer sequences
PY  - 2001
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2001__4_1_a3/
LA  - en
ID  - JIS_2001__4_1_a3
ER  - 
%0 Journal Article
%A Sixdeniers, J.-M.
%A Penson, K.A.
%A Solomon, A.I.
%T Extended Bell and Stirling numbers from hypergeometric exponentiation
%J Journal of integer sequences
%D 2001
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2001__4_1_a3/
%G en
%F JIS_2001__4_1_a3
Sixdeniers, J.-M.; Penson, K.A.; Solomon, A.I. Extended Bell and Stirling numbers from hypergeometric exponentiation. Journal of integer sequences, Tome 4 (2001) no. 1. http://geodesic.mathdoc.fr/item/JIS_2001__4_1_a3/