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Catalan Numbers, the Hankel Transform, and Fibonacci Numbers

2002; University of Waterloo; Volume: 5; Issue: 1 Linguagem: Inglês

1530-7638

Aleksandar Cvetković, Predrag M. Rajković, Miloÿs Ivkovic,

Mathematical functions and polynomials

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. Thisisdonebyflndingtheexplicitformforthecoe‐cientsinthethree-termrecurrence relation that the corresponding orthogonal polynomials satisfy.