An interesting class of Hankel determinants

Johann Cigler; Mike Tyson

paper

An interesting class of Hankel determinants

arXiv:1807.08330

Abstract

For small $r$ the Hankel determinants $d_{r} (n)$ of the sequence $((n 2 n + r))_{n \geq 0}$ are easy to guess and show an interesting modular pattern. For arbitrary $r$ and $n$ no closed formulae are known, but for each positive integer $r$ the special values $d_{r} (r n)$ , $d_{r} (r n + 1)$ , and $d_{r} (r n + ⌊ \frac{r + 1}{2} ⌋)$ have nice values which will be proved in this paper.

20 pages