Generating Functions for Extended Stirling Numbers of the First Kind
Department of Mathematics
In this paper we extend the definition of Stirling numbers of the first
kind by way of a special multiset. This results in a family of number
triangles for which we show how to obtain ordinary generating functions
for the rows and exponential generating functions for the columns. The
latter are derived via a recursive process. We also indicate how to
obtain formulas, in terms of factorials, generalized harmonic numbers,
and polynomials, for the entries in the columns of these number
Full version: pdf,
(Concerned with sequences
Received January 3 2014;
revised version received April 27 2014.
Published in Journal of Integer Sequences, May 11 2014.
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