English

Some relatives of the Catalan sequence

Combinatorics 2021-11-22 v1 Probability

Abstract

We study a family of sequences cn(a2,,ar)c_n(a_2,\ldots,a_r), where r2r\ge2 and a2,,ara_2,\ldots,a_r are real parameters. We find a sufficient condition for positive definiteness of the sequence cn(a2,,ar)c_n(a_2,\ldots,a_r) and check several examples from OEIS. We also study relations of these sequences with the free and monotonic convolution.

Cite

@article{arxiv.1907.10725,
  title  = {Some relatives of the Catalan sequence},
  author = {Elżbieta Liszewska and Wojciech Młotkowski},
  journal= {arXiv preprint arXiv:1907.10725},
  year   = {2021}
}
R2 v1 2026-06-23T10:30:00.087Z