ON SUMS WITH THE r-DERANGEMENT NUMBERS
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Published:2023-06-30
Issue:2
Volume:23
Page:469-480
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ISSN:2068-3049
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Container-title:Journal of Science and Arts
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language:en
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Short-container-title:J. Sci. Arts
Author:
ÖMÜR NEŞE1, SÜDEMEN KÜBRANUR1, KOPARAL SİBEL2, DURAN ÖMER1
Affiliation:
1. University of Kocaeli, Faculty of Art and Science, Department of Mathematics, 41380 Kocaeli, Turkey. 2. University of Bursa Uludağ, Faculty of Art and Science, Department of Mathematics, 16059 Bursa, Turkey.
Abstract
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 (α) by using the generating functions and Riordan arrays. For example, for n,r∈Z^+with n≥r,
∑_(i=0)^(n-r)〖(-1)^i ((r+1i)) (D_r (n-i))/(n-i)!〗=(-1)^(n-r)/(n-r)!.
Publisher
Valahia University of Targoviste - Journal of Science and Arts
Subject
General Earth and Planetary Sciences,General Environmental Science
Reference21 articles.
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