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Motzkin Numbers

✍ Scribed by M. Aigner

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
178 KB
Volume
19
Category
Article
ISSN
0195-6698

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✦ Synopsis

In this paper Motzkin numbers M n (which are related to Catalan numbers) are studied. The (known) connection to Tchebychev polynomials is discussed with applications to the Hankel matrices of Motzkin numbers. It is shown that the sequence M n is logarithmically concave with lim M n+1 /M n = 3. Finally, two ballot-number type sequences for M n are derived, with an application to directed animals.

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