Combinatorics of Generalized Motzkin Numbers
Yi Wang and Zhi-Hai Zhang
School of Mathematical Sciences
Dalian University of Technology
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.
Full version: pdf,
(Concerned with sequences
November 19 2014; revised version received December 17 2014.
Published in Journal of Integer Sequences, January 24 2015.
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