Geodesic
Sums of Powers and Special Polynomials
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 2, pp. 275-283

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In this paper, we discuss sums of powers 1p + 2p + ... + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their connection to other interesting series. In particular, we show their connection to an interesting problem of Ovidiu Furdui.
Keywords: sum of powers, exponential polynomial, geometric polynomial, generating function, harmonic numbers, exponential integral function 
Boyadzhiev, Khristo N. Sums of Powers and Special Polynomials. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 2, pp. 275-283. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_2_a10/
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[1] K.N. Boyadzhiev, Close encounters with the Stirling numbers of the second kind, Math. Mag. 85 (2012) 252–266.

[2] K.N. Boyadzhiev, Exponential polynomials, Stirling numbers, and evaluation of some Gamma integrals, Abstract and Applied Analysis, Volume 2009, Article ID 168672 (electronic). doi:10.1155/2009/168672

[3] K.N. Boyadzhiev, A Series transformation formula and related polynomials, Int. J. Math. and Math. Sci. 2005 (23) (2005) 3849–3866. doi:10.1155/IJMMS.2005.3849

[4] K.N. Boyadzhiev, Polyexponentials, (2007), at https://arxiv.org/abs/0710.1332

[5] K.N. Boyadzhiev and A. Dil, Geometric polynomials: properties and applications to series with zeta values, Anal. Math. 42 (2016) 203–224. doi:10.1007/s10476-016-0302-y

[6] O. Furdui, Problem 96, Mathproblems 4 (2014) 263. Solutions in 4 (2014) 304–308.

[7] A.P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, Integrals and Series, vol. 1 Elementary Functions (Gordon and Breach, 1986).

[8] R. Witula, K. Kaczmarek, P. Lorenc, E. Hetmaniok and M. Pleszczyński, Jordan numbers, Stirling numbers, and sums of powers, Discuss. Math. General Alg. and Appl. 34 (2014) 155–166. doi:10.7151/dmgaa.1225