Geodesic
Iterative procedure for hypersums of powers of integers
Journal of integer sequences, Tome 17 (2014) no. 5.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Relying on a recurrence relation for the hypersums of powers of integers put forward recently, we develop an iterative procedure which allows us to express a hypersum of arbitrary order in terms of ordinary (zeroth order) power sums. Then, we derive the coefficients of the hypersum polynomial as a function of the Bernoulli numbers and the Stirling numbers of the first kind.
Classification : 11B57, 11C08, 11Y55
Keywords: hypersum polynomial, iterative procedure, elementary symmetric polynomial, Bernoulli number, Stirling number of the first kind 
@article{JIS_2014__17_5_a6,
     author = {Cereceda, Jos\'e Luis},
     title = {Iterative procedure for hypersums of powers of integers},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
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     number = {5},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_5_a6/}
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Cereceda, José Luis. Iterative procedure for hypersums of powers of integers. Journal of integer sequences, Tome 17 (2014) no. 5. http://geodesic.mathdoc.fr/item/JIS_2014__17_5_a6/