On an extension of the Genocchi numbers
type: Item
instance of: scholarly article
title: On an extension of the Genocchi numbers
zbMATH Open document ID: 0823.05004
DOI: 10.1016/S0195-6698(95)90053-5
author: Arthur Randrianarivony
author: Dominique Dumont
published in: European Journal of Combinatorics
publication date: 1995-10-23T00:00:00Z
review text: The authors investigate the sequence of polynomials \(B_ n(x, y)\) defined by the recurrence \[ B_ 1(x, y)= 1,\;B_ n(x, y)= (x+ 1)(y+ 1) B_{n- 1}(x+ 1, y+ 1)- xyB_{n- 1}(x, y) \] which was introduced initially by Stieltjes and mentioned by Touchard. This sequence turns out to be a generalization of the Gandhi polynomials [\textit{J. M. Gandhi}, Am. Math. Mon. 77, 505-506 (1970; Zbl 0198.370)] which generate the Genocchi numbers. A generating function for \(B_ n(x, y)\) is obtained, including a representation by a continued fraction. Another expression of \(B_ n(x, y)\) is given in terms of maximal points of surjective mappings of the sequence \((1, 2,\dots, 2n)\). For related problems see the same authors [Discrete Math. 132, No. 1-3, 37-49 (1994; Zbl 0807.05001)].
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 759652
zbMATH Keywords: polynomials
zbMATH Keywords: Gandhi polynomials
zbMATH Keywords: Genocchi numbers
zbMATH Keywords: generating function
zbMATH Keywords: continued fraction
MaRDI profile type: Publication
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full work available at URL: s0195-6698(95)90053-5
OpenAlex ID: W2340104141
description: scientific article; zbMATH DE number 759652