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Catalan Numbers, The Hankel Transform, And Fibonacci Numbers

2002; Institute of Electrical and Electronics Engineers; Linguagem: Inglês

0250-4162

Aleksandar Cvetković, Predrag M. Rajković, Miloÿs Ivkovic,

Advanced Mathematical Identities

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.