New Expressions for Sums of Products of the Catalan Numbers

Abstract

In this paper, we perform a further investigation for the Catalan numbers. By making use of the method of derivatives and some properties of the Bell polynomials, we establish two new expressions for sums of products of arbitrary number of the Catalan numbers. The results presented here can be regarded as the development of some known formulas.

Keywords

• Catalan numbers
• Bell polynomials
• combinatorial identities