The Central Coefficients of a Family of Pascal-like Triangles and Colored Lattice Paths
School of Science
Waterford Institute of Technology
We study the central coefficients of a family of Pascal-like triangles
defined by Riordan arrays. These central coefficients count left-factors
of colored Schröder paths. We give various forms of the generating
function, including continued fraction forms, and we calculate their
Hankel transform. By using the A and Z sequences of the defining
Riordan arrays, we obtain a matrix whose row sums are equal to the
central coefficients under study. We explore the row polynomials of this
matrix. We give alternative formulas for the coefficient array of the
sequence of central coefficients.
Full version: pdf,
(Concerned with sequences
Received July 28 2018; revised version received December 19 2018.
Published in Journal of Integer Sequences,
December 19 2018.
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