Extended Bell and Stirling numbers from hypergeometric exponentiation

Details Extended Bell and Stirling numbers from hypergeometric exponentiation Extended Bell and Stirling numbers from hypergeometric exponentiation

2001-06-14

arxiv.org/abs/math/0106123v1

Mathematics

Combinatorics

12 pages, Latex. Journal of Integer Sequences (in press)

Scientific paper

Exponentiating the hypergeometric series gives a recursion relation for integer sequences which are generalizations of conventional Bell numbers. The corresponding associated Stirling numbers of the second kind are also generated and investigated. For the lowest order generalisation, one can give a combinatorial interpretation of these 'Bell' numbers, and of some Stirling numbers associated with them. We also consider these analogues of Bell numbers in the case of restricted partitions.

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