Cvetković, Aleksandar; Rajković, Predrag; Ivković, Milos Catalan numbers, the Hankel transform, and Fibonacci numbers. (English) Zbl 1041.11014 J. Integer Seq. 5, No. 1, Art. 02.1.3, 8 p. (2002). The authors prove that the Hankel transformation of a sequence whose \(n\)th element is the sum of the \(n\)th and \((n+1)\)th Catalan numbers is a subsequence of the Fibonacci numbers. They do this by finding the explicit form for the coefficients in the tree-term recurrence relation that the corresponding orthogonal polynomials satisfy. Reviewer: Andreas N. Philippou (Patras) Cited in 1 ReviewCited in 23 Documents MSC: 11B65 Binomial coefficients; factorials; \(q\)-identities 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 05A10 Factorials, binomial coefficients, combinatorial functions 44A15 Special integral transforms (Legendre, Hilbert, etc.) Software:OEIS PDFBibTeX XMLCite \textit{A. Cvetković} et al., J. Integer Seq. 5, No. 1, Art. 02.1.3, 8 p. (2002; Zbl 1041.11014) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: a(n) = 3*a(n-1) - a(n-2) for n >= 2, with a(0) = a(1) = 1. F(2n) = bisection of Fibonacci sequence: a(n) = 3*a(n-1) - a(n-2). Sum of adjacent Catalan numbers.