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Research Article | Open Access

Some identities involving derangement polynomials and r-Bell polynomials

Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China
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Abstract

In this paper two kinds of identities involving derangement polynomials and r-Bell polynomials were established. The identities of the first kind extended the identity on derangement numbers and Bell numbers due to Clarke and Sved and its generalizations due to Du and Fonseca. The identities of the second kind extended some of the results on derangement polynomials and Bell polynomials due to Kim et al.

Keywords

derangement polynomialsr-Bell polynomialsStirling numbersidentities
CLC number: 05A10, 05A19, 11B83

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 2051-2062
DOI: 10.3934/math.2024102

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Cite this article:
Xu A. Some identities involving derangement polynomials and r-Bell polynomials. AIMS Mathematics, 2024, 9(1): 2051-2062. https://doi.org/10.3934/math.2024102

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Received: 29 September 2023
Revised: 28 November 2023
Accepted: 12 December 2023
Published: 15 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)