Catalan Numbers and Jacobi Polynomials
Combinatorics
2020-08-26 v3
Abstract
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.
Cite
@article{arxiv.2005.08939,
title = {Catalan Numbers and Jacobi Polynomials},
author = {Thomas M. Richardson},
journal= {arXiv preprint arXiv:2005.08939},
year = {2020}
}
Comments
11 pages Version 3, minor typo in a reference corrected