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
USA
Abstract:
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.
Full version: pdf,
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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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