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Das Bernoullische Potenzsummen-Problem und die Stirling-Zahlen.
(REPORT HAS BEEN WITHDRAWN)

by R. Brawer and M. Pirovino

(Report number 1991-01)

Abstract
We prove in this paper the formula \begin{eqnarray*}\sum_{m=0}^nm^k = \sum_{p=0}^k{n+1\choose p+1}S_{pk}\,p!\end{eqnarray*}for the sum of the $\,k\,$-th powers. Here $\, S_{pk}\,p,k\in\Nn$ denote theStirling numbers of the second kind.

Keywords: combinatorics, sums of powers, Stirling numbers of the second kind

@Techreport{BP91_1,
  author = {R. Brawer and M. Pirovino},
  title = {Das Bernoullische Potenzsummen-Problem und die Stirling-Zahlen.
 (REPORT HAS BEEN WITHDRAWN)},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1991-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1991/1991-01.pdf },
  year = {1991}
}

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