Simplifying coefficients in differential equations for generating function of Catalan numbers

Abstract

In the paper, by the Faà di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients in two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers.

Keywords

• simplifying
• coefficient
• nonlinear ordinary differential equation
• generating function
• catalan number
• faà di bruno formula
• bell polynomial of the second kind
• inversion theorem