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

Department of Mathematics

College of Sciences

Gabès University

Tunisia

**Abstract:**

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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