Article
Application of Fa´a Di Bruno’s Formula in the Construction of Combinatorial Identities
Journal of Combinatorics and Number Theory
(2015)
Abstract
Chou, Hsu, and Shiue in [3] use Fa`a di Bruno’s formula give a class of composite series expansions. In this paper, we apply those expansions to construct a class of identities for Catalan numbers, large Schroder numbers, small Schroder numbers, parametric Catalan numbers, Stirling numbers, binomial numbers, some other recursive
number sequences, and recursive polynomial sequences.
Keywords
- Fa´a di Bruno’s Formula,
- Catalan numbers,
- large Schr¨oder numbers,
- small Schr¨oder numbers,
- Stirling numbers,
- binomial numbers,
- recursive number sequences,
- generalized Gegenbauer-Humbert polynomials
Disciplines
Publication Date
2015
Publisher Statement
The Journal of Combinatorics and Number Theory is published by Nova Science Publishers. For more information please see the Journal of Combinatorics and Number Theory homepage.
Citation Information
Tian-Xiao He. "Application of Fa´a Di Bruno’s Formula in the Construction of Combinatorial Identities" Journal of Combinatorics and Number Theory Vol. 7 Iss. 3 (2015) p. 65 - 84 ISSN: 1942-5600 Available at: http://works.bepress.com/tian_xiao_he/80/