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A direct method for evaluating some nice Hankel determinants and proofs of several conjectures

Xiang-Ke Chang Xing-Biao Hu Ying-Nan Zhang

Dynamical Systems mathscidoc:1912.43173

Linear Algebra and its Applications, 438, (5), 2523-2541, 2013.3
In this paper, we propose a direct method to evaluate Hankel determinants for some generating functions satisfying a certain type of quadratic equations, which cover generating functions of Catalan numbers, Motzkin numbers and Schrder numbers. Additionally, four recent conjectures proposed by Cigler (2011) [3] are proved.
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@inproceedings{xiang-ke2013a,
  title={A direct method for evaluating some nice Hankel determinants and proofs of several conjectures},
  author={Xiang-Ke Chang, Xing-Biao Hu, and Ying-Nan Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112729395547733},
  booktitle={Linear Algebra and its Applications},
  volume={438},
  number={5},
  pages={2523-2541},
  year={2013},
}
Xiang-Ke Chang, Xing-Biao Hu, and Ying-Nan Zhang. A direct method for evaluating some nice Hankel determinants and proofs of several conjectures. 2013. Vol. 438. In Linear Algebra and its Applications. pp.2523-2541. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112729395547733.
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