Combinatorial identities with multiple harmonic-like numbers

TL;DR

This paper explores multiple harmonic-like numbers through generating functions, deriving closed-form binomial sum identities and connecting them with hyperharmonic and odd harmonic numbers.

Contribution

It introduces new closed-form identities for binomial sums involving harmonic-like numbers and links them to other prominent sequences.

Findings

Closed-form expressions for binomial sums with harmonic-like numbers

Derivation of combinatorial identities involving hyperharmonic and odd harmonic numbers

Presentation of corollaries and examples illustrating main results

Abstract

Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are immediate consequences of the main result. Finally, combinatorial identities involving harmonic-like numbers and other prominent sequences like hyperharmonic numbers and odd harmonic numbers are offered.