A106183 Expansion of 1/sqrt(1-4x-4x^2+16x^3).

1, 2, 8, 24, 88, 304, 1120, 4096, 15328, 57536, 218112, 830208, 3176704, 12196352, 46982144, 181452800, 702465536, 2724948992, 10589474816, 41217216512, 160657903616, 627019489280, 2449986043904, 9583049572352, 37519931654144

Offset

0,2

Comments

Diagonal sums of number triangle A067804. In general, a(n)=sum{k=0..floor(n/2), C(2k,k)C(2(n-2k),n-2k)*r^k} has g.f. 1/sqrt(1-4x-4r*x^2+16r*x^3).

Links

Table of n, a(n) for n=0..24.

Formula

a(n)=sum{k=0..floor(n/2), C(2k, k)C(2(n-2k), n-2k)}.

D-finite with recurrence: n*a(n) +2*(1-2*n)*a(n-1) +4*(1-n)*a(n-2) +8*(2*n-3)*a(n-3)=0. - R. J. Mathar, Nov 09 2012

a(n) ~ 2^(2*n+1) / sqrt(3*Pi*n). - Vaclav Kotesovec, Feb 03 2014

Mathematica

CoefficientList[Series[1/Sqrt[1-4*x-4*x^2+16*x^3], {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 03 2014 *)

Crossrefs

Sequence in context: A094038 A007223 A106189 * A357160 A362139 A060899

Adjacent sequences: A106180 A106181 A106182 * A106184 A106185 A106186

Keyword

easy,nonn

Author

Paul Barry, Apr 24 2005

Status

approved