Geodesic
Hyper-sums of powers of integers and the Akiyama-Tanigawa matrix
Journal of integer sequences, Tome 8 (2005) no. 2
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.
Classification : 11Y55, 11B68
Keywords: Bernoulli numbers, Stirling numbers, power sums 
@article{JIS_2005__8_2_a1,
     author = {Inaba,  Yoshinari},
     title = {Hyper-sums of powers of integers and the {Akiyama-Tanigawa} matrix},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {2},
     zbl = {1073.11009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a1/}
}
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Inaba,  Yoshinari. Hyper-sums of powers of integers and the Akiyama-Tanigawa matrix. Journal of integer sequences, Tome 8 (2005) no. 2. http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a1/