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URL: https://oeis.org/A115969

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A115969
Expansion of 1/(2*sqrt(1-6*x+x^2) - 1).
1
1, 6, 44, 336, 2600, 20232, 157864, 1233528, 9646328, 75470472, 590627208, 4623006744, 36189493080, 283315538664, 2218082213544, 17365909807416, 135964585370552, 1064534233678920, 8334838664902600, 65258529915843672, 510950805474456344, 4000571712415431336
OFFSET
0,2
LINKS
FORMULA
G.f.: A(x)^2/(2*A(x) - A(x)^2) where A(x) is the g.f. of the central Delannoy numbers A001850.
D-finite with recurrence: 3*n*a(n) + 3*(9-14*n)*a(n-1) + (151*n-225)*a(n-2) + 12*(9-4*n)*a(n-3) + 4*(n-3)*a(n-4) = 0. - R. J. Mathar, Nov 14 2011
a(n) ~ (1/3 + 2/sqrt(33)) * (4+2*sqrt(33)/3)^n. - Vaclav Kotesovec, Feb 01 2014
MATHEMATICA
CoefficientList[Series[1/(2*Sqrt[1-6*x+x^2]-1), {x, 0, 30}], x] (* Vaclav Kotesovec, Feb 01 2014 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(1/(2*sqrt(1-6*x+x^2)-1)) \\ G. C. Greubel, May 05 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/(2*Sqrt(1-6*x+x^2)-1) )); // G. C. Greubel, May 05 2019
(SageMath) (1/(2*sqrt(1-6*x+x^2)-1)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 05 2019
CROSSREFS
Sequence in context: A227665 A102591 A114935 * A082412 A108452 A363104
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 03 2006
STATUS
approved