Journal of Integer Sequences, Vol. 17 (2014), Article 14.5.3

Iterative Procedure for Hypersums of Powers of Integers

José Luis Cereceda
Distrito Telefónica, Edificio Este 1
28050 Madrid


Relying on a recurrence relation for the hypersums of powers of integers put forward recently, we develop an iterative procedure which allows us to express a hypersum of arbitrary order in terms of ordinary (zeroth order) power sums. Then, we derive the coefficients of the hypersum polynomial as a function of the Bernoulli numbers and the Stirling numbers of the first kind.

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(Concerned with sequences A008275.)

Received October 14 2013; revised versions received January 19 2014; March 17 2014. Published in Journal of Integer Sequences, March 23 2014.

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