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)=\sum_{n=1}^{\infty}((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 Mez\H{o} and Dil. 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. 
Ayhan Dil and Khristo N. Boyadzhiev
math.NT math.CA