Some new binomial sums related to the Catalan triangle

Abstract

In this paper, we derive ma= n+1 (iden)ities on the classical Catalan triangle are the well-known ballot numbers. The first three types are based on the determinant and the fourth is relied on the permanent of a square matrix. It not only produces many known and new identities involving Catalan numbers, but also provides a new viewpoint on combinatorial triangles.