Geodesic
Extended Bell and Stirling numbers from hypergeometric exponentiation
Journal of integer sequences, Tome 4 (2001) no. 1
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.
Classification : 11B73, 33C20
Mots-clés : extended Bell numbers, Stirling numbers, recurrence relations 
@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},
     year = {2001},
     volume = {4},
     number = {1},
     zbl = {0973.11023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2001__4_1_a3/}
}
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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/