Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.3

Catalan Numbers, the Hankel Transform, and Fibonacci Numbers

Aleksandar Cvetkovic
Faculty of Electrical Engineering
University of Nis, Yugoslavia
e-mail: aca@elfak.ni.ac.yu

Predrag Rajkovic
Faculty of Mechanical Engineering
University of Nis, Yugoslavia
e-mail: nispeca@yahoo.com

Milos Ivkovic
IMECC-UNICAMP, C.P. 6065, 13083-970
Campinas-SP, Brazil
e-mail: milos@ime.unicamp.br

Abstract: We prove that the Hankel transformation of a sequence whose elements are the sums of two adjacent Catalan numbers is a subsequence of the Fibonacci numbers. This is done by finding the explicit form for the coefficients in the three-term recurrence relation that the corresponding orthogonal polynomials satisfy.

(Concerned with sequences A005807 A001906 A001519

Received April 8, 2002; revised version received May 14, 2002. Published in Journal of Integer Sequences May 14, 2002.