It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants. We also give several of their arithmetical and/or combinatorial properties and applications. These concepts can be generalized in the case of hyperharmonic numbers.
Harmonic numbers, hyperharmonic numbers, recurrence relations, determinants, convolutions
KOMATSU, TAKAO and Pizarro-Madariaga, Amalia
"Harmonic numbers associated with inversion numbers in terms of determinants,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 27.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/27