Journal of Integer Sequences, Vol. 14 (2011), Article 11.5.1

Hankel Transforms of Linear Combinations of Catalan Numbers

Michael Dougherty, Christopher French, Benjamin Saderholm, and Wenyang Qian
Department of Mathematics and Statistics
Grinnell College
Grinnell, IA 50112


Cvetković, Rajković, and Ivković proved that the Hankel transform of the sequence of sums of adjacent Catalan numbers is the bisection of the sequence of Fibonacci numbers. Here, we find recurrence relations for the Hankel transform of more general linear combinations of Catalan numbers, involving up to four adjacent Catalan numbers, with arbitrary coefficients. Using these, we make certain conjectures about the recurrence relations satisfied by the Hankel transform of more extended linear combinations.

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(Concerned with sequences A000159 A014523 A103433.)

Received January 28 2011; revised version received April 5 2011. Published in Journal of Integer Sequences, April 20 2011.

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