Identities between harmonic, hyperharmonic and Daehee numbers

J Inequal Appl. 2018;2018(1):168. doi: 10.1186/s13660-018-1757-0. Epub 2018 Jul 11.

Abstract

In this paper, we present some identities relating the hyperharmonic, the Daehee and the derangement numbers, and we derive some nonlinear differential equations from the generating function of a hyperharmonic number. In addition, we use this differential equation to obtain some identities in which the hyperharmonic numbers and the Daehee numbers are involved.

Keywords: Daehee numbers; Differential equation; Hyperharmonic numbers.