A New Characterization of Catalan Numbers Related to Hankel Transforms and Fibonacci Numbers
Department of Mathematics
College of Sciences
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.
Full version: pdf,
(Concerned with sequences
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.
Journal of Integer Sequences home page