Some identities on the Catalan, Motzkin and Schroder numbers

被引：11
|
作者：
Deng, Eva Y. P. [1 ]
Yan, Wei-Jun [2 ]
机构：
[1] Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China
[2] Neusoft Inst Informat, Dept Fdn Courses, Dalian 116023, Peoples R China
来源：
DISCRETE APPLIED MATHEMATICS | 2008年 / 156卷 / 14期
关键词：
Catalan number; Motzkin number; Schroder number; Riordan group;
D O I：
10.1016/j.dam.2007.11.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, some identities between the Catalan, Motzkin and Schroder numbers are obtained by using the Riordan group. We also present two combinatorial proofs for an identity related to the Catalan numbers with the Motzkin numbers and an identity related to the Schroder numbers with the Motzkin numbers, respectively. (C) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码：2781 / 2789
页数：9
相关论文
共 50 条
  • [1] Some Convolution Identities for Catalan Numbers
    Rakhimov, I
    Atan, Mohd K. A.
    Hadi, N. A.
    MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES, 2022, 16 (04): : 771 - 782
  • [2] When Numerical Analysis Crosses Paths with Catalan and Generalized Motzkin Numbers
    Eloe, Paul
    Kublik, Catherine
    JOURNAL OF INTEGER SEQUENCES, 2018, 21 (08)
  • [3] On divisibility properties of some differences of Motzkin numbers
    Lengyel, Tamas
    ANNALES MATHEMATICAE ET INFORMATICAE, 2013, 41 : 121 - 136
  • [4] Some combinatorial identities containing central binomial coefficients or Catalan numbers*
    Qi, Feng
    Niu, Da-Wei
    Lim, Dongkyu
    APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING, 2023, 31 (01):
  • [5] Motzkin and Catalan Tunnel Polynomials
    Barnabei, Marilena
    Bonetti, Flavio
    Castronuovo, Niccole
    Silimbani, Matteo
    JOURNAL OF INTEGER SEQUENCES, 2018, 21 (08)
  • [6] Some congruences on Delannoy numbers and Schroder numbers
    Liu, Ji-Cai
    Li, Long
    Wang, Su-Dan
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (07) : 2035 - 2041
  • [7] Three Identities of the Catalan-Qi Numbers
    Mahmoud, Mansour
    Qi, Feng
    MATHEMATICS, 2016, 4 (02)
  • [8] Several series identities involving the Catalan numbers
    Yin, Li
    Qi, Feng
    TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2018, 172 (03) : 466 - 474
  • [9] THE INVERSE OF A TRIANGULAR MATRIX AND SEVERAL IDENTITIES OF THE CATALAN NUMBERS
    Qi, Feng
    Zou, Qing
    Guo, Bai-Ni
    APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2019, 13 (02) : 518 - 541
  • [10] ANALOGUES OF SEVERAL IDENTITIES AND SUPERCONGRUENCES FOR THE CATALAN-QI NUMBERS
    Zou, Qing
    JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS, 2016, 7 (04): : 235 - +
12345