Table of Contents
Journal of Numbers
Volume 2014, Article ID 158351, 6 pages
http://dx.doi.org/10.1155/2014/158351
Research Article

Sums of Products Involving Power Sums of Integers

Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India

Received 12 November 2013; Accepted 22 January 2014; Published 27 February 2014

Academic Editor: Junesang Choi

Copyright © 2014 Jitender Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A sequence of rational numbers as a generalization of the sequence of Bernoulli numbers is introduced. Sums of products involving the terms of this generalized sequence are then obtained using an application of Faà di Bruno's formula. These sums of products are analogous to the higher order Bernoulli numbers and are used to develop the closed form expressions for the sums of products involving the power sums which are defined via the Möbius function μ and the usual power sum of a real or complex variable . The power sum is expressible in terms of the well-known Bernoulli polynomials by .