Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.7

Hyper-Sums of Powers of Integers and the Akiyama-Tanigawa Matrix

Yoshinari Inaba
Toba Senior High School
Nishikujo, Minami-ku
Kyoto 601-8449
Japan

Abstract: In this short essay, we consider hyper-sums of powers of integers, namely sums of power sums. We can obtain easily their formulae as polynomials by using formulae for ordinary sums of powers of integers. The coefficient of the first-degree term in each polynomial coincides with the matrix element of the Akiyama-Tanigawa matrix.

(Concerned with sequences A008275 and A008277 .)

Received January 5 2005; revised version received March 9 2005; April 1 2005; April 29 2005. Published in Journal of Integer Sequences May 17 2005.