Geodesic
On some generalizations of sum of powers of natural numbers
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 31-44

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In this paper we consider some generalizations of the sum of powers of natural numbers. In particular, we study the class of sums whose generating function is the power of the generating function for the classical sums of powers. We also consider the so-called binomial sums and solve the problem of constructing polynomials that allow to calculate the values of the corresponding sums in certain cases.
Keywords: sums of powers of natural numbers, Bernoulli numbers, Genocchi numbers, Gandhi polynomials. 
@article{IVM_2019_8_a3,
     author = {A. K. Svinin and S. V. Svinina},
     title = {On some generalizations of sum of powers of natural numbers},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {31--44},
     publisher = {mathdoc},
     number = {8},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_8_a3/}
}
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A. K. Svinin; S. V. Svinina. On some generalizations of sum of powers of natural numbers. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 31-44. http://geodesic.mathdoc.fr/item/IVM_2019_8_a3/