Some applications of the generalized Eulerian numbers

被引：5

作者：

Rzadkowski, Grzegorz ^{[1
]}

Urlinska, Malgorzata ^{[2
]}

机构：

[1] Warsaw Univ Technol, Dept Finance & Risk Management, Ludwika Narbutta 85, PL-00999 Warsaw, Poland

[2] Warsaw Univ Technol, Fac Math & Comp Sci, Koszykowa 75, PL-00662 Warsaw, Poland

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2019年 / 163卷

关键词：

Eulerian number; Second-order Eulerian number; Bernoulli number; Autonomous differential equation; Integral representation; BERNOULLI NUMBERS; POLYNOMIALS;

D O I：

10.1016/j.jcta.2018.11.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is related to an autonomous first-order differential equation, solutions of which are used to obtain integral representations of some numbers, including the Bernoulli numbers. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：85 / 97

页数：13

共 24 条

[1]

[Anonymous], EXPRESSIONS INVOLVIN

[2]

[Anonymous], 2007, ANAL MATH

[3]

[Anonymous], 1736, Comment. Acad. Sci. Petrop

[4]

[Anonymous], 1958, An Introduction to Combinatorial Analysis

[5]

[Anonymous], 2006, P ICNAAM 2006

[6]

[Anonymous], The On-Line Encyclopedia of Integer Sequences-A338706-Number of 2-linear trees on n nodes

[7] Bivariate generating functions for a class of linear recurrences: General structure [J].

Barbero G, J. Fernando ;

Salas, Jesus ;

Villasenor, Eduardo J. S. .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2014, 125 :146-165

[8] COMBINATORIAL PROPERTY OF Q-EULERIAN NUMBERS [J].

CARLITZ, L .

AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (01) :51-54

[9]

CARLITZ L, 1954, T AM MATH SOC, V76, P332

[10]

Chung F, 2010, J COMB, V1, P29

← 1 2 3 →