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Hankel determinants of sums of consecutive Motzkin numbers

✍ Scribed by Naiomi T. Cameron; Andrew C.M. Yip

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 466 KB
Volume: 434
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.09.031

No coin nor oath required. For personal study only.

✦ Synopsis

We use combinatorial methods to evaluate Hankel determinants for the sequence of sums of consecutive t-Motzkin numbers. More specifically, we consider the following determinant:

where t is a real number and m t k is the total weight of all paths from (0, 0) to (k, 0) that stay above the x-axis and use up and down steps of weight one and level steps of weight t.

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