Sixdeniers, J. -M.; Penson, K. A. and Solomon, A. I.
Extended Bell and Stirling numbers from hypergeometric exponentiation.
Journal of Integer Sequences, 4(1)
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Exponentiating the hypergeometric series
0FL(1,1,...,1;z), L = 0,1,2,..., furnishes a recursion relation for the members of certain integer sequences
bL(n), n = 0,1,2,.... For L >= 0, the bL(n)'s are generalizations of the conventional Bell numbers, b0(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 b1(n) and of some Stirling numbers associated with them. We also consider the L>1 analogues of Bell numbers for restricted partitions.
||2001 The Authors
||integer sequences; Bell numbers; Stirling numbers; hypergeometric series
||Science > Physical Sciences
||21 Jun 2007
||16 Jun 2014 00:51
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