A unified approach for the Hankel determinants of classical combinatorial numbers

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

Elouafi, Mohamed

关键词: Hankel determinant;    Orthogonal polynomials;    Chebyshev polynomials;    Catalan numbers;    Motzkin numbers;    Schroder numbers;   

DOI  :  10.1016/j.jmaa.2015.06.034

来源: Elsevier

【 摘 要 】

We give a general formula for the determinants of a class of Hankel matrices which arise in combinatorics theory. We revisit and extend existent results on Hankel determinants involving the sum of consecutive Catalan, Motzkin and Schroder numbers and we prove a conjecture of [10] about the recurrence relations satisfied by the Hankel transform of linear combinations of Catalans numbers. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free