A115969 Expansion of 1/(2*sqrt(1-6*x+x^2) - 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

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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
(Sage) (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

Adjacent sequences: A115966 A115967 A115968 * A115970 A115971 A115972

Keyword

easy,nonn

Author

Paul Barry, Feb 03 2006

Status

approved