Some nice Hankel determinants

Details Some nice Hankel determinants Some nice Hankel determinants

2011-09-07

arxiv.org/abs/1109.1449v2

Mathematics

Combinatorics

45 pages

Scientific paper

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.

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