Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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.


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.


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


Computer Science and Mathematics, Computational Mathematics

Comments (1)

Comment 1
Received: 16 September 2019
Commenter: (Click to see Publons profile: )
Commenter's Conflict of Interests: I am the first and corrsponding author.
Comment: This preprint has been formally published as

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
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