Combinatorial Identities with Multiple Harmonic-like Numbers

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.

Keywords

• multiple harmonic-like numbers
• harmonic number
• binomial transform