Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.8

An Explicit Formula for Sums of Powers of Integers in Terms of Stirling Numbers


Diffalah Laissaoui
Dr Yahia Farés University of Médéa
26000 Médéa
Algeria

Mourad Rahmani
Faculty of Mathematics
University of Sciences and Technology
Houari Boumediene
P. O. Box 32
El Alia
Bab Ezzouar
16111 Algiers
Algeria

Abstract:

In this note we present an explicit formula for the sum of powers of the first n terms of a general arithmetic sequence in terms of Stirling numbers. We then provide an algorithm for calculating the sum of consecutive powers of integers.

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Received October 26 2016; revised version received February 24 2017. Published in Journal of Integer Sequences, February 24 2017.

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