Hankel Transforms of Linear Combinations of Catalan Numbers
Michael Dougherty, Christopher French, Benjamin Saderholm, and Wenyang Qian
Department of Mathematics and Statistics
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.
Full version: pdf,
(Concerned with sequences
Received January 28 2011;
revised version received April 5 2011.
Published in Journal of Integer Sequences, April 20 2011.
Journal of Integer Sequences home page