Journal of Integer Sequences, Vol. 16 (2013), Article 13.3.2

Generalized Akiyama-Tanigawa Algorithm for Hypersums of Powers of Integers

José Luis Cereceda
Distrito Telefónica, Edificio Este 1
28050 Madrid


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 crr ,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.

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(Concerned with sequences A008275 A008277.)

Received November 12 2012; revised version received February 11 2013. Published in Journal of Integer Sequences, March 2 2013.

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