ON SUMS WITH THE.r-DERANGEMENT NUMBERS

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ÖMÜR N., Sudemen K., Koparal S., Duran O.

JOURNAL OF SCIENCE AND ARTS, sa.2, ss.469-480, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2023
  • Doi Numarası: 10.46939/j.sci.arts-23.2-a14
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.469-480
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this paper, we derive some sums involving the r-derangement numbers, D-r (n) and the generalized hyperharmonic numbers of order r,H-n(r) (alpha) by using the generating functions and Riordan arrays. For example, for n,r epsilon Z(+) with n >= r, Sigma(n-r)(i=0) (-1)(i) (r+1/i) Dr(n-i)/(n-i)!= (-1)(n-r)/(n-r)!