Catalan-like Numbers and Determinants

Abstract

A class of numbers, called Catalan-like numbers, are introduced which unify many well-known counting coefficients, such as the Catalan numbers, the Motzkin numbers, the middle binomial coefficients, the hexagonal numbers, and many more. Generating functions, recursions and determinants of Hankel matrices are computed, and some interpretations are given as to what these numbers count. © 1999 Academic Press.