# Computation and theory of Euler sums of generalized hyperharmonic numbers

## TL;DR

This paper derives explicit formulas for sums of generalized hyperharmonic numbers, expressing them in terms of multiple zeta values, harmonic numbers, and Stirling numbers, extending previous results on harmonic number sums.

## Contribution

It introduces new explicit formulas for sums involving generalized hyperharmonic numbers with complex index sequences, connecting them to multiple zeta values and Stirling numbers.

## Key findings

- Expressed sums in terms of multiple zeta values and harmonic numbers
- Extended previous formulas to more complex index sequences
- Provided explicit formulas for generalized hyperharmonic sums

## Abstract

Recently, Dil and Boyadzhiev \cite{AD2015} proved an explicit formula for the sum of multiple harmonic numbers whose indices are the sequence $\left( {{{\left\{ 0 \right\}}_r},1} \right)$. In this paper we show that the sums of multiple harmonic numbers whose indices are the sequence $\left( {{{\left\{ 0 \right\}}_r,1};{{\left\{ 1 \right\}}_{k-1}}} \right)$ can be expressed in terms of (multiple) zeta values, multiple harmonic numbers and Stirling numbers of the first kind, and give an explicit formula.