Generalized Akiyama-Tanigawa Algorithm for Hypersums of Powers of Integers
José Luis Cereceda
Distrito Telefónica, Edificio Este 1
In this paper we consider the hypersum polynomials
Pk(m)(n) = Σr=0k+m+1 crr,m nr,
and give an explicit formula for the coefficients
,m. We show that the crr
,m satisfy a generalized Akiyama-Tanigawa
recurrence relation, thus extending some previous results due to Inaba.
We also give a number of identities involving the Stirling numbers of
the first and second kinds, as well as Bernoulli and harmonic numbers.
Full version: pdf,
(Concerned with sequences
Received November 12 2012;
revised version received February 11 2013.
Published in Journal of Integer Sequences, March 2 2013.
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