Journal of Integer Sequences, Vol. 16 (2013), Article 13.3.3

A New Characterization of Catalan Numbers Related to Hankel Transforms and Fibonacci Numbers

Belgacem Bouras
Department of Mathematics
College of Sciences
Gabès University


Cvetković, Rajković, and Ivković proved that the Hankel transform of the sequence of sums of two successive Catalan numbers is the sequence of Fibonacci numbers with odd indices. Later, Benjamin, Cameron, Quinn, and Yerger extended this result, and proved that if we remove one term from this sequence of sums, then the Hankel transform is the sequence of Fibonacci numbers with even indices. In this paper, we prove that the Catalan numbers are the unique nonnegative integer sequence satisfying this property.

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(Concerned with sequences A000159 A014523 A103433.)

Received July 11 2012; revised versions received October 23 2012; December 28 2012; February 3 2013. Published in Journal of Integer Sequences, March 2 2013.

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