Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.4

Combinatorics of Generalized Motzkin Numbers

Yi Wang and Zhi-Hai Zhang
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024
PR China


The generalized Motzkin numbers are common generalizations of the Motzkin numbers and the Catalan numbers. We investigate their combinatorial properties, including the combinatorial interpretation, the recurrence relation, the binomial transform, the Hankel transform, the log-convexity, the continued fraction of the generating function, and the total positivity of the corresponding Hankel matrix.

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(Concerned with sequences A000108 A001006 A002212 A126120.)

Received November 19 2014; revised version received December 17 2014. Published in Journal of Integer Sequences, January 24 2015.

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