Sums involving generalized harmonic and Daehee numbers

Abstract

In this paper, we establish some sums involving generalized harmonic and Daehee numbers which are derived from the generating functions. For example, for $n, r\geq 1,$ \begin{eqnarray*} \sum_{i=0}^{n}H\left( i,r-1,\alpha \right) H_{n-i}^{r}\left( \alpha \right) &=&\sum_{l_{1}+l_{2}+ \cdots +l_{r+1}=n}H_{l_{1}}(\alpha )H_{l_{2}}(\alpha ) \cdots H_{l_{r+1}}(\alpha ). \end{eqnarray*}