2016/05/19 by Taekyun Kim, Kim, Taekyun, Dae San Kim +1
Computer Science · Mathematics · #05A19 #11B37 #11B83 #34A34 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1605.05927
openalex publication_date 2016/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce two differential equations arising from the generating function of the Catalan numbers which are `inverses' to each other in some sense. From these differential equations, we obtain some new and explicit identities for Catalan and higher-order Catalan numbers. In addition, by other means than differential equations we also derive some interesting identities involving Catalan numbers which are of arithmetic and combinatorial nature.