On some generalized geometric sequences, stirling numbers and euler polynomials

Gorowski, J.; Lomnicki, A.; Gorowski, J; Lomnicki, A

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On some generalized geometric sequences, stirling numbers and euler polynomials

Gorowski, J.; Lomnicki, A.

Ars Combinatoria 138: 233-247

2018

ISSN/ISBN: 0381-7032

Accession: 105430326

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Summary

Some consistent formulas for the finite sums nΣj=1(j+μ)kqj and nΣj=1 (j+μk)qj are obtained by a new approach, namely by investigating a geometric sequence. Additionally an identity for the Stirling numbers of the second kind was derived and, as a consequence, some divisibility property for these numbers was received.