Computation and theory of Euler sums of generalized hyperharmonic numbers

Abstract

Recently, Dil and Boyadzhiev [10] proved an explicit formula for the sum of multiple harmonic numbers whose indices are the sequence ({0}r,1). In this paper, we show that the sums of multiple harmonic numbers whose indices are the sequence ({0}r,1;{1}k−1) can be expressed in terms of (multiple) zeta values, (multiple) harmonic numbers, and Stirling numbers of the first kind, and give an explicit formula.