Simplifying coefficients in differential equations for generating function of Catalan numbers

被引：10
|
作者：
Qi, Feng [1 ,2 ,3 ]
Yao, Yong-Hong [3 ]
机构：
[1] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Henan, Peoples R China
[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao 028043, Inner Mongolia, Peoples R China
[3] Tianjin Polytech Univ, Sch Math Sci, Tianjin 300387, Peoples R China
来源：
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE | 2019年 / 13卷 / 01期
关键词：
Simplifying; coefficient; nonlinear ordinary differential equation; generating function; Catalan number; Faa di Bruno formula; Bell polynomial of the second kind; inversion theorem; BELL POLYNOMIALS; SPECIAL VALUES; FAMILY; FORMULAS;
D O I：
10.1080/16583655.2019.1663782
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In the paper, by the Faa di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients in two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers.
引用
收藏
页码：947 / 950
页数：4
相关论文
共 44 条
  • [11] EXPLICIT FORMULAS FOR DERANGEMENT NUMBERS AND THEIR GENERATING FUNCTION
    Qi, Feng
    Guo, Bai-Ni
    JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2016,
  • [12] A SIMPLE FORM FOR COEFFICIENTS IN A FAMILY OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS
    Qi, Feng
    ADVANCES AND APPLICATIONS IN MATHEMATICAL SCIENCES, 2018, 17 (08): : 555 - 561
  • [13] Combinatorial Interpretations of Lucas Analogues of Binomial Coefficients and Catalan Numbers
    Bennett, Curtis
    Carrillo, Juan
    Machacek, John
    Sagan, Bruce E.
    ANNALS OF COMBINATORICS, 2020, 24 (03) : 503 - 530
  • [14] Combinatorial Interpretations of Lucas Analogues of Binomial Coefficients and Catalan Numbers
    Curtis Bennett
    Juan Carrillo
    John Machacek
    Bruce E. Sagan
    Annals of Combinatorics, 2020, 24 : 503 - 530
  • [15] Series with Central Binomial Coefficients,Catalan Numbers,and Harmonic Numbers
    Boyadzhiev, Khristo N.
    JOURNAL OF INTEGER SEQUENCES, 2012, 15 (01)
  • [16] The Asymptotics of Factorials, Binomial Coefficients and Catalan Numbers
    Kessler, David A.
    Schiff, Jeremy
    JOURNAL OF INTEGER SEQUENCES, 2021, 24 (08)
  • [17] 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):
  • [18] Some properties of the Catalan-Qi function related to the Catalan numbers
    Qi, Feng
    Mahmoud, Mansour
    Shi, Xiao-Ting
    Liu, Fang-Fang
    SPRINGERPLUS, 2016, 5
  • [19] CONVOLUTION IDENTITIES INVOLVING THE CENTRAL BINOMIAL COEFFICIENTS AND CATALAN NUMBERS
    Batir, Necdet
    Kucuk, Hakan
    Sorgun, Sezer
    TRANSACTIONS ON COMBINATORICS, 2021, 10 (04) : 225 - 238
  • [20] Some limit properties for the coefficients of the q-Catalan numbers
    Zikai Wu
    Hongxia Du
    Indian Journal of Pure and Applied Mathematics, 2014, 45 : 469 - 478
12345