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 A219312 Composition of the binomial transform of Fibonacci numbers and the Catalan transform of Fibonacci numbers. 6
 0, 1, 4, 15, 59, 243, 1034, 4501, 19920, 89281, 404184, 1844789, 8477571, 39183625, 182010366, 849115811, 3976405347, 18684473203, 88060677880, 416162484693, 1971567963673, 9361218368921, 44539107835094, 212308063827055, 1013779444844754, 4848597239921803 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Paul Barry, A Catalan transform and related transformations on integer sequences, pp. 20-22. FORMULA G.f.: (sqrt(5*x-1) - sqrt(x-1))/(2*((x-1)*sqrt(5*x-1) - x*sqrt(x-1))). a(n) ~ 5^(n+5/2)/(8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Sep 19 2013 MATHEMATICA CoefficientList[Series[(Sqrt[5*x-1] - Sqrt[x-1])/(2*((x-1)*Sqrt[5*x-1] - x*Sqrt[x-1])), {x, 0, 20}], x] (* Vaclav Kotesovec, Sep 19 2013 *) PROG (PARI) Vec((sqrt(5*x-1) - sqrt(x-1))/(2*((x-1)*sqrt(5*x-1) - x*sqrt(x-1))) + O(x^25)) \\ G. C. Greubel, Jan 28 2017 CROSSREFS Cf. A000045. Sequence in context: A326212 A199210 A129155 * A271752 A291244 A290910 Adjacent sequences: A219309 A219310 A219311 * A219313 A219314 A219315 KEYWORD easy,nonn AUTHOR Arkadiusz Wesolowski, Nov 17 2012 STATUS approved

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Last modified June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)