Hankel determinants for convolution powers of Catalan numbers
Discrete Mathematics(2019)
摘要
The Hankel determinants r2(i+j)+r2(i+j)+ri+j0≤i,j≤n−1 of the convolution powers of Catalan numbers were considered by Cigler and Krattenthaler. We evaluate these determinants for r≤31 by finding shifted periodic continued fractions, which arose in application of Sulanke and Xin’s continued fraction method. These include some of the conjectures of Cigler as special cases. We also conjecture a polynomial characterization of these determinants. The same technique is used to evaluate the Hankel determinants 2(i+j)+ri+j0≤i,j≤n−1. Similar results are obtained.
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关键词
Hankel determinants,Continued fractions
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