Dyck Paths, Motzkin Paths, and the Binomial Transform
Stefano Capparelli and Alberto Del Fra
Università di Roma La Sapienza
We study the moments of orthogonal polynomial sequences (OPS) arising
from tridiagonal matrices. We obtain combinatorial information about
the sequence of moments of some OPS in terms of Motzkin and Dyck
paths, and also in terms of the binomial transform. We then introduce
an equivalence relation on the set of Dyck paths and some operations on
them. We determine a formula for the cardinality of those equivalence
classes, and use this information to obtain a combinatorial formula for
the number of Dyck and Motzkin paths of a fixed length.
Full version: pdf,
(Concerned with sequences
Received May 19 2015;
revised versions received July 19 2015; July 27 2015.
Published in Journal of Integer Sequences, July 29 2015.
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