Extended Bell and Stirling numbers from hypergeometric exponentiationReport as inadecuate

Author: J. -M. Sixdeniers, K. A. Penson and A. I. Solomon

Source: https://core.ac.uk/


Exponentiating the hypergeometric series \ud <sub>0</sub>F<sub>L</sub>(1,1,...,1;z), L = 0,1,2,..., furnishes a recursion relation for the members of certain integer sequences \ud b<sub>L</sub>(n), n = 0,1,2,....
For L >= 0, the b<sub>L</sub>(n)'s are generalizations of the conventional Bell numbers, b<sub>0</sub>(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<sub>1</sub>(n) and of some Stirling numbers associated with them.
We also consider the L>1 analogues of Bell numbers for restricted partitions ...

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