Some nice Hankel determinants

Abstract

I study Hankel determinants of a class of sequences which can be interpreted as generalizations of the Catalan numbers and the central binomial coefficients. They follow a modular pattern with a frequent appearance of zeroes, so that the theory of orthogonal polynomials is not applicable. Even so our theorems and conjectures show some similarity with the relations between Catalan numbers and Fibonacci polynomials or between central binomial coefficients and Lucas polynomials.

45 pages

References in corpus (3)

• q-Lucas polynomials and associated Rogers-Ramanujan type identities
• A simple approach to some Hankel determinants
• Hankel determinants of Schroeder-like numbers

Cited by in corpus (5)

• Hankel determinant solutions to several discrete integrable systems and the Laurent Property
• A special class of Hankel determinants
• Some elementary observations on Narayana polynomials and related topics
• Hankel determinants for convolution powers of Catalan numbers
• Hankel determinants and shifted periodic continued fractions