Taylor expansions for Catalan and Motzkin numbers

Sen Peng Eu, Shu Chung Liu, Yeong Nan Yeh*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

13 引文 斯高帕斯(Scopus)

摘要

In this paper we introduce two new expansions for the generating functions of Catalan numbers and Motzkin numbers. The novelty of the expansions comes from writing the Taylor remainder as a functional of the generating function. We give combinatorial interpretations of the coefficients of these two expansions and derive several new results. These findings can be used to prove some old formulae associated with Catalan and Motzkin numbers. In particular, our expansion for Catalan number provides a simple proof of the classic Chung-Feller theorem; similar result for the Motzkin paths with flaws is also given.

原文英語
頁(從 - 到)345-357
頁數13
期刊Advances in Applied Mathematics
29
發行號3
DOIs
出版狀態已發佈 - 2002 十月

ASJC Scopus subject areas

  • 應用數學

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