组合序列的moment问题是组合学中一类重要的研究课题。它与全正性理论及连分式理论有着密切的联系。本项目将综合运用组合学、分析学和代数学的方法和技巧来研究组合序列的moment性质，研究内容围绕以下三个部分展开。.1.Catalan-like数的moment性质研究：本项目将借助Catalan-like数这个平台来集中处理组合序列的moment性质，进一步给出Catalan-like数的moment性质的判别法。.2.Apéry数的moment性质研究：本项目将利用Apéry数的组合背景、Hankel行列式、Lindström–Gessel-Viennot方法等来研究关于Apéry数的猜想。.3.递归序列的moment性质研究：本项目将综合运用组合计数、代数技巧、分析工具研究递归序列的发生函数的连分式表示，进而给出递归序列的moment性质的一些判断法则。

The moment problem of combinatorial sequences is an important topic in combinatorics. Moment problems of combinatorial sequences are closely related to total positivity and continued fraction. The goal of this project is to study the moment problem of combinatorial sequences via analytic techniques, combinatorial approaches and algebraic methods. The content of the project is divided into three parts..1. Catalan-like numbers unify many well-known combinatorial sequences, including Catalan numbers, Motzkin numbers, Schröder numbers and so on. We will give some criterions for moment property of Catalan-like numbers ..2. We will use Lindström–Gessel-Viennot method, the Hankel determinants and combinatorial interpretations of Apéry numbers to research the moment property of Apéry numbers.We will study conjectures on the Apéry numbers..3. Combinatorial sequences are usually recursive sequences that satisfy certain recursive relations. We will use combinatorial enumerations, algebraic skills and analytic tools to study the continued fraction expansion of generating functions of recursive sequences. Then get some criterions for moment property of recurrence sequences.