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Closed Forms for Derangement Numbers in Terms of the Hessenberg Determinants
Version 1
: Received: 11 October 2016 / Approved: 11 October 2016 / Online: 11 October 2016 (10:53:07 CEST)
A peer-reviewed article of this Preprint also exists.
Abstract
In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.
Keywords
derangement number; closed form; Hessenberg determinant; tridiagonal determinant; generating function; recurrence relation; derivative
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Honest John China
The commenter has declared there is no conflict of interests.
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the corresponding author of this paper.
Feng Qi, Jiao-Lian Zhao, and Bai-Ni Guo, Closed forms for derangement numbers in terms of the Hessenberg determinants, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales-Serie A: Matemáticas 112 (2018), in press; Available online at http://dx.doi.org/10.1007/s13398-017-0401-z.
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author of this paper.
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