AI 中文总结
本文计算了源于非相交Motzkin meander加权计数的类卡特兰序列的移位汉克尔行列式，其中部分为新发现或已被提出，还应用其验证了Cigler与Krattenthaler的猜想二项式行列式恒等式。
AI 中文摘要
本文计算了类卡特兰序列的（移位）汉克尔行列式，这类序列自然产生于非相交Motzkin meander的加权计数中。在这些行列式计算中，1.5个是新发现的，具有通用移位汉克尔行列式；2个已由Cigler和Krattenthaler以等价组合形式早期提出；其余为Cigler所猜想。作为应用，我们进一步验证了Cigler与Krattenthaler提出的一个猜想二项式行列式恒等式。
英文摘要
In this paper, we compute the (shifted) Hankel determinants of Catalan-like sequences, which arise naturally from the weighted enumerations of nonintersecting Motzkin meanders. Among these determinant evaluations, one and a half are newly discovered, featuring generic shifted Hankel determinants; two were formulated earlier by Cigler and Krattenthaler in an equivalent combinatorial form; and the rest were conjectured by Cigler. As an application, we further confirm a conjectural binomial determinant identity proposed by Cigler and Krattenthaler.
