Geodesic
Iterative procedure for hypersums of powers of integers
Journal of integer sequences, Tome 17 (2014) no. 5
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},
     year = {2014},
     volume = {17},
     number = {5},
     zbl = {1360.11047},
     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/