Recently, Thomas and Namboothiri [1] derived a recurrence identity expressing an exponential power sum with negative powers in terms of another exponential power sum with positive powers. From this result, the authors obtained a corresponding recurrence relation for the ordinary power sums  In this short note, we provide an alternative simple proof of the latter recurrence. Our proof is based on the following two ingredients: (i) an expression for and (ii) the symmetry property of the power sum polynomials

sums of powers of integers, recursive formula, odd powers, even powers, symmetry of the power sum polynomials.

Received: May 9, 2023; Revised: May 22, 2023; Accepted: June 6, 2023; Published: June 10, 2023

How to cite this article: José L. Cereceda, On a recurrence relation for the sums of powers of integers, Far East Journal of Mathematical Education 24 (2023), 45-50. http://dx.doi.org/10.17654/0973563123011

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References
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