Journal of Integer Sequences, Vol. 21 (2018), Article 18.2.7

Combinatorial Identities for Generalized Stirling Numbers Expanding f-Factorial Functions and the f-Harmonic Numbers

Maxie D. Schmidt
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332


We introduce a class of f(t)-factorials, or f(t)-Pochhammer symbols, that includes many, if not most, well-known factorial and multiple factorial function variants as special cases. We consider the combinatorial properties of the corresponding generalized classes of Stirling numbers of the first kind that arise as the coefficients of the symbolic polynomial expansions of these f-factorial functions. The combinatorial properties of these more general parameterized Stirling number triangles include analogs of known expansions of the ordinary Stirling numbers by p-order harmonic number sequences, through the definition of a corresponding class of p-order f-harmonic numbers.

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(Concerned with sequences A000142 A000165 A001008 A001147 A002805 A006882 A007318 A008275 A008517 A094638.)

Received March 29 2017; revised version received February 24 2018. Published in Journal of Integer Sequences, March 7 2018.

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