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.51 Chihara, T.S., (1978) An Introduction to Orthogonal Polynomials, , Gordon and Breach, New YorkGautschi, W., Orthogonal polynomials: Applications and computations (1996) Acta Numerica, 1996, pp. 45-119. , Cambridge University PressEncyclopedia of Combinatorial Structures, , http://algo.inria.fr/bin/encyclopodia?Search=ESCnb&argseach=431Krattenthaler, C., Advanced Determinant Calculus, , http://www.mat.iinivie.ac.at/People/kratt/artikel/detsurv.htmlLayman, J.W., The hankel transform and some of its properties (2001) Journal of Integer Sequences, 4. , Article 01.1.5Peart, P., Woan, W.J., Generating functions via hankel and stieltjes matrices (2000) Journal of Integer Sequences, 3 (2). , Article 00.2.1Woan, W.J., (2001) Hankel Matrices and Lattice Paths, Journal of Integer Sequences, 4. , Article 01.1.2Santos, J.P.O., Ivković, M., Fibonacci numbers and partitions Fibonacci Quarterly, , to appearSzegö, G., (1975) Orthogonal Polynomials, 23. , AMS, 4th. ed. (Colloquium publications)Sloane, N.J.A., The On-line Encyclopedia of Integer Sequences, , http://www.research.att.com/~njas/sequences/Tosić, R., (1999) Kombinatorika (in Serbian), , Univerzitet u Novom Sadu, Novi SadVajda, S., (1989) Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, , Halsted PressZeilberger, D., Amdeberhan, T., DODGSON: A Maple Package for Conjecturing and Proving Determinant Identities by Dodgson's Condensation Method, , http://astro.ocis.temple.edu/doron/programs.html