Some Sums Involving Generalized Harmonic and r-Derangement Numbers

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koparal s.

Cumhuriyet Science Journal, cilt.45, sa.1, ss.111-116, 2024 (Hakemli Dergi) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.17776/csj.1365360
  • Dergi Adı: Cumhuriyet Science Journal
  • Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.111-116
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In this paper, we derive some sums involving generalized harmonic and r-derangement numbers by using generating functions of these numbers and some combinatorial identities. The relationship between Daehee numbers and generalized harmonic numbers of rank r, H(n,r,α) is given. In addition, sums including Daehee numbers of order r,D_n^r, generalized hyperharmonic numbers of order r, H_n^r (α), Cauchy numbers of order r, C_n^r and the stirling numbers of the first kind, s(n,i) are also calculated.