Sums of Consecutive Powers as a Linear Combination of Products of Two Figurate Numbers
František Marko
Department of Mathematics
The Pennsylvania State University
76 University Drive
Hazleton, PA 18202
USA
Abstract:
We derive two formulae expressing the pth power of an integer
n as a linear combination of products of two figurate numbers of
dimensions not exceeding p. Then we derive two formulae for the
sum of the pth powers of the first n consecutive natural
numbers as a linear combination of products of two figurate numbers of
dimensions not exceeding p.
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(Concerned with sequences
A008277
A019538.)
Received July 25 2021; revised version received, March 6 2022.
Published in Journal of Integer Sequences,
March 6 2022.
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