A105865 Expansion of (1/(1-2*x^2))*c(x/(1-2*x^2)), where c(x) is the g.f. of A000108.

1, 1, 4, 9, 30, 94, 328, 1165, 4294, 16134, 61752, 239610, 940716, 3729324, 14908176, 60026109, 243211206, 990897478, 4057013080, 16683617326, 68879236036, 285388549188, 1186296731376, 4945790840338, 20675513743900, 86648395759516

Offset

0,3

Links

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

Formula

G.f.: (1-sqrt((1-4*x-2*x^2)/(1-2*x^2)))/(2*x).

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

Conjecture: (n+1)*a(n) +2(1-2n)*a(n-1) +4*(1-n)*a(n-2) +4*(2n-3)*a(n-3) +4*(n-3)*a(n-4)=0. - R. J. Mathar, Dec 13 2011

a(n) ~ 3^(1/4) * (2+sqrt(6))^(n+1) / (2^(9/4) * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 01 2014

G.f.: 1/G(x), with G(x) = 1-2*x^2-(x-x^3)/(1-x^2-(x-x^3)/G(x)) (continued fraction). - Nikolaos Pantelidis, Jan 09 2023

Mathematica

CoefficientList[Series[(1-Sqrt[(1-4*x-2*x^2)/(1-2*x^2)])/(2*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)

Prog

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

Crossrefs

Sequence in context: A151270 A149113 A149114 * A187983 A230056 A069103

Adjacent sequences: A105862 A105863 A105864 * A105866 A105867 A105868

Keyword

easy,nonn

Author

Paul Barry, Apr 23 2005

Status

approved