Journal of Integer Sequences, Vol. 15 (2012), Article 12.3.3

Two Catalan-type Riordan Arrays and their Connections to the Chebyshev Polynomials of the First Kind

Asamoah Nkwanta and Earl R. Barnes
Department of Mathematics
Morgan State University
Baltimore, MD 21251


Riordan matrix methods and properties of generating functions are used to prove that the entries of two Catalan-type Riordan arrays are linked to the Chebyshev polynomials of the first kind. The connections are that the rows of the arrays are used to expand the monomials (1/2)(2x)n and (1/2)(4x)n in terms of certain Chebyshev polynomials of degree n. In addition, we find new integral representations of the central binomial coefficients and Catalan numbers.

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(Concerned with sequence A000012 A000108 A000984 A001700 A001791 A002054 A002694 A003516 A007318 A030053 A039598 A094527 A094531 A111418)

Received December 8 2011; revised version received February 6 2012. Published in Journal of Integer Sequences, March 11 2012.

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