Article
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The Generating Function of the Catalan Numbers and Lower Triangular Integer Matrices
Version 1
: Received: 18 November 2017 / Approved: 20 November 2017 / Online: 20 November 2017 (07:20:26 CET)
A peer-reviewed article of this Preprint also exists.
Abstract
In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.
Keywords
simplification; coefficient; nonlinear ordinary differential equation; generating function; Catalan number; inverse matrix; lower triangular integer matrix; Faά di Bruno formula; Bell polynomial of the second kind; inversion theorem
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Feng Qi and Yong-Hong Yao, Simplifying coefficients in differential equations for generating function of Catalan numbers, Journal of Taibah University for Science 13 (2019), no. 1, 947--950; available online at https://doi.org/10.1080/16583655.2019.1663782