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

Predrag Rajkovic
Faculty of Mechanical Engineering
University of Nis, Yugoslavia

Milos Ivkovic
IMECC-UNICAMP, C.P. 6065, 13083-970
Campinas-SP, Brazil

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.

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(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.

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