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.
Full version: pdf,
(Concerned with sequences
Received March 29 2017; revised version received February 24 2018.
Published in Journal of Integer Sequences, March 7 2018.
Journal of Integer Sequences home page