Catalan-like numbers and Hausdorff moment sequences
Abstract
In this paper we show that many well-known counting coefficients, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the central Delannoy numbers are Hausdorff moment sequences in a unified approach. In particular we answer a conjecture of Liang at al. which such numbers have unique representing measures. The smallest interval including the support of representing measure is explicitly found. Subsequences of Catalan-like numbers are also considered. We provide a necessary and sufficient condition for a pattern of subsequences that if sequences are the Stieltjes Catalan-like numbers, then their subsequences are Stieltjes Catalan-like numbers. Moreover, a representing measure of a linear combination of consecutive Catalan-like numbers is studied.
Keywords
Cite
@article{arxiv.1809.07523,
title = {Catalan-like numbers and Hausdorff moment sequences},
author = {Hayoung Choi and Yeong-Nan Yeh and Seonguk Yoo},
journal= {arXiv preprint arXiv:1809.07523},
year = {2018}
}