2020/05/18 by Thomas M. Richardson, Richardson, Thomas M.
Mathematics · Physics and Astronomy · #05A10 #15B36 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #math.CO #msc:05A10 #msc:15B36
paper · pdf · doi:10.48550/arxiv.2005.08939
11 pages Version 3, minor typo in a reference corrected
openalex publication_date 2020/05/18 · arxiv created 2020/08/25 · arxiv updated 2020/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the inverse of the Hankel matrix of the reciprocals of the Catalan numbers has integer entries. We generalize the result to an infinite family of generalized Catalan numbers. The Hankel matrices that we consider are associated with orthogonal polynomials that are variants of Jacobi polynomials. Our proofs use these polynomials and computer algebra based on Wilf-Zeilberger theory.