Euler sums of hyperharmonic numbers

The hyperharmonic numbers h(n)((r)) are defined by means of the classical harmonic numbers. We show that the Euler-type sums with hyperharmonic numbers: sigma(r, m) = Sigma(infinity)(n=1) h(n)((r))/n(m) can be expressed in terms of series of Hurwitz zeta function values. This is a generalization of a result of Mezo and Dil (2010) [7]. We also provide an explicit evaluation of sigma(r, m) in a closed form in terms of zeta values and Stirling numbers of the first kind. Furthermore, we evaluate several other series involving hyperharmonic numbers. (C) 2014 Elsevier Inc. All rights reserved.