A106185 Expansion of 1/sqrt(1-4*x-12*x^2+48*x^3).

1, 2, 12, 32, 160, 480, 2208, 7104, 31104, 104960, 444928, 1554432, 6444544, 23112704, 94341120, 345243648, 1393754112, 5181456384, 20755267584, 78122680320, 311231840256, 1183024939008, 4695356866560, 17987367075840

Offset

0,2

Comments

In general, a(n) = Sum_{k=0..floor(n/2)} C(2*k,k)*C(2*(n-2*k),n-2*k)*r^k has g.f. 1/sqrt(1-4*x-4*r*x^2+16r*x^3).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = Sum_{k=0..floor(n/2)} C(2*k,k)*C(2*(n-2*k), n-2*k)*3^k.

D-finite with recurrence: n*a(n) +2*(1-2n)*a(n-1)+12*(1-n)*a(n-2)+24*(2n-3)*a(n-3)= 0. - R. J. Mathar, Dec 08 2011

a(n) ~ 2^(2*n+1)/sqrt(Pi*n). - Vaclav Kotesovec, Oct 17 2012

Mathematica

CoefficientList[Series[1/Sqrt[1-4x-12x^2+48x^3], {x, 0, 40}], x] (* Harvey P. Dale, Jun 21 2011 *)

Prog

(PARI) x='x+O('x^50); Vec(1/sqrt(1-4*x-12*x^2+48*x^3)) \\ G. C. Greubel, Mar 16 2017

Crossrefs

Sequence in context: A358852 A363661 A133577 * A098203 A305330 A320542

Adjacent sequences: A106182 A106183 A106184 * A106186 A106187 A106188

Keyword

easy,nonn

Author

Paul Barry, Apr 24 2005

Status

approved