Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.4

Generating Functions for Extended Stirling Numbers of the First Kind

Martin Griffiths
Department of Mathematics
Christ’s College
Christchurch 8013
New Zealand


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 triangles.

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(Concerned with sequences A008284 A035098 A130534.)

Received January 3 2014; revised version received April 27 2014. Published in Journal of Integer Sequences, May 11 2014.

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