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.
Hankel determinants of convolution powers of Catalan numbers revisited
Hankel determinants for convolution powers of Catalan numbers
Some observations about determinants which are connected with Catalan numbers and related topics
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