Hankel determinants for generating functions of Catalan-like numbers
Hankel determinants for generating functions of Catalan-like numbers
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DOI：
10.1080/03081087.2017.1422690
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发表时间：
2019-03
影响因子：
1.1
通讯作者：
L. L. Liu-L.;Lili Mu
中科院分区：
文献类型：
--
作者：
L. L. Liu-L.;Lili Mu
设是Catalan-like数的生成函数。我们证明了相应的Hankel行列式满足三项递归关系。作为应用，我们给出了Catalan数、中心二项式系数、大小Schröder数等经典组合计数系数的Hankel行列式的统一表示.
Abstract Let be the generating functions of Catalan-like numbers . We show that the corresponding Hankel determinants satisfy a three-term recurrence relation. As applications, we express the Hankel determinants of some classical combinatorial counting coefficients, including the Catalan numbers, the central binomial coefficients, the large and little Schröder numbers, in a unified way.