A219312 Composition of the binomial transform of Fibonacci numbers and the Catalan transform of Fibonacci numbers.

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

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