Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can be expressed in terms of r-Stirling numbers, leading to combinatorial interpretations of many interesting identities.
© 2003 Arthur T. Benjamin
Benjamin, A.T., Gaebler, D., & Gaebler R. (2003). A combinatorial approach to hyperharmonic numbers. Integers: The Electronic Journal of Combinatorial Number Theory, 3: 1-9.