涉及中心二项式系数和加泰罗尼亚数的卷积恒等式

IF 0.6 Q3 MATHEMATICS Transactions on Combinatorics Pub Date : 2021-01-01 DOI:10.22108/TOC.2021.127505.1821

Necdet Batır, Hakan Küçük, Sezer Sorgun

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引用次数: 3

摘要

推广了Witula和Qi等人的卷积恒等式。涉及中心二项式系数和加泰罗尼亚数字。我们的公式允许我们建立许多新的身份涉及这些重要的量，并恢复一些已知的身份在文献中。同时，我们给出了夏皮罗的加泰罗尼亚卷积和一个著名的Haj'{o}s恒等式的新证明。

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Convolution identities involving the central binomial coefficients and Catalan numbers

We generalize some convolution identities due to Witula and Qi et al‎. ‎involving the central binomial coefficients and Catalan numbers‎. ‎Our formula allows us to establish many new identities involving these important quantities‎, ‎and recovers some known identities in the literature‎. ‎Also‎, ‎we give new proofs of Shapiro's Catalan convolution and a famous identity of Haj'{o}s‎.

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