A new approach to Catalan numbers using differential equations
Number Theory
2016-05-20 v1
Abstract
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.
Cite
@article{arxiv.1605.05927,
title = {A new approach to Catalan numbers using differential equations},
author = {Taekyun Kim and Dae San Kim},
journal= {arXiv preprint arXiv:1605.05927},
year = {2016}
}
Comments
12 pages