Preprint Article Version 1 This version not peer reviewed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)

How to cite: Qi, F.; Qin, X..; Yao, Y. The Generating Function of the Catalan Numbers and Lower Triangular Integer Matrices. Preprints 2017, 2017110120 (doi: 10.20944/preprints201711.0120.v1). Qi, F.; Qin, X..; Yao, Y. The Generating Function of the Catalan Numbers and Lower Triangular Integer Matrices. Preprints 2017, 2017110120 (doi: 10.20944/preprints201711.0120.v1).

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.

Subject Areas

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

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