与Narayana多项式及q=-1时的q-Narayana多项式相关的一些序列和数三角
Some sequences and number triangles which are related to Narayana polynomials and to q-Narayana polynomials for q=-1
AI总结：
本研究围绕与Narayana多项式及q=-1时q-Narayana多项式相关的数序列、数三角展开，探究有界Dyck路径的对应权重，获得相关结果与猜想。
AI中文摘要：
众所周知，Catalan数可被解释为Dyck路径的数量；类似地，Narayana多项式和q=-1时的q-Narayana多项式可被解释为这些路径的某些权重。本注记试图获取有界Dyck路径对应权重的相关信息，这也引出了一些此前在其他情境中出现过的数序列及Pascal三角的类似物；我们考察了若干例子，得到了一些结果和猜想。
英文摘要：
As is well known the Catalan numbers can be interpreted as numbers of Dyck paths. The Narayana polynomials and the q-Narayana polynomials for q=-1 can analogously be interpreted as certain weights of these paths. In the present note we try to get some information about the corresponding weights of bounded Dyck paths. This also leads to some number sequences and analogues of Pascals triangle which previously have occurred in other contexts. We consider some examples and obtain some results and conjectures.
