  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.
