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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
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
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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