Divisibility of Generalized Catalan Numbers and Raney Numbers

The Raney numbers, also called Fuss-Catalan numbers, are defined by Rk(n, r) = r(...)/(kn + r). A generalized Lobb numbers is introduced. The relationship between Raney numbers and generalized Lobb numbers and the relationship between generalized Lobb numbers and generalized Catalan numbers are given. Based on the relationships among Raney numbers, generalized Lobb numbers, and generalized Catalan numbers, we present the divisibility of a certain class of those numbers.