Some experimental observations about Hankel determinants of convolution powers of Catalan numbers

TL;DR

This paper presents conjectures about Hankel determinants related to convolution powers of Catalan numbers, based on computer experiments, and invites others to prove these unverified hypotheses.

Contribution

It introduces new conjectures on Hankel determinants of convolution powers of Catalan numbers derived from computational experiments, lacking formal proofs.

Findings

Conjectures about Hankel determinants of convolution powers of Catalan numbers.

Empirical evidence from computer experiments supporting these conjectures.

Open invitation for proofs and further research.

Abstract

Computer experiments suggest some conjectures about Hankel determinants of convolution powers of Catalan numbers. Unfortunately, for most of them I have no proofs. I would like to present them anyway hoping that someone finds them interesting and can prove them.