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 a certain 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.
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Kim, D.S., Kim, T. A new approach to Catalan numbers using differential equations. Russ. J. Math. Phys. 24, 465–475 (2017). https://doi.org/10.1134/S1061920817040057
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DOI: https://doi.org/10.1134/S1061920817040057