Journal of Integer Sequences, Vol. 22 (2019), Article 19.1.3

The Central Coefficients of a Family of Pascal-like Triangles and Colored Lattice Paths

Paul Barry
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.

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(Concerned with sequences A000108 A000984 A001405 A001700 A007318 A008288 A026003 A054341 A060693 A060899 A081577 A107230 A110109.)

Received July 28 2018; revised version received December 19 2018. Published in Journal of Integer Sequences, December 19 2018.

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