Divisibility of Generalized Catalan Numbers and Raney Numbers

Authors

Jacob Bobrowski, University of Nevada, Las Vegas
Tianxiao He, Illinois Wesleyan UniversityFollow
Peter Jau Shyong Shiue, University of Nevada, Las VegasFollow

Document Type

Article

Publication Date

6-1-2019

Publication Title

Journal of Computational Analysis and Applications

Volume

26

Issue

6

First page number:

1047

Last page number:

1058

Abstract

The Raney numbers, also called Fuss-Catalan numbers, are dened by Rk(n, r) = r (kn+r n)/ (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.

Keywords

Catalan numbers; Divisibility; Fuss-Catalan numbers; Generalized catalan numbers; Generalized lobb numbers; Lobb numbers; Raney numbers

Disciplines

Applied Mathematics

Language

English

Repository Citation

Bobrowski, J., He, T., Shiue, P. J. (2019). Divisibility of Generalized Catalan Numbers and Raney Numbers. Journal of Computational Analysis and Applications, 26(6), 1047-1058.