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A179648
Expansion of (1/(1+4x-2x^2))*c(x/(1+4x-2x^2)), c(x) the g.f. of A000108.
1
1, -3, 12, -47, 190, -778, 3224, -13475, 56710, -239986, 1020200, -4353430, 18636908, -80004388, 344264624, -1484499811, 6413133638, -27750688914, 120258432264, -521833284514, 2267084792708, -9859984425324, 42925569027408
OFFSET
0,2
COMMENTS
Hankel transform is the (4,5) Somos-4 sequence A174404.
LINKS
FORMULA
G.f.: (1/(2*x))*(1-sqrt((1-2*x^2)/(1+4*x-2*x^2))) = (sqrt(2*x^2-4*x-1)-sqrt(2*x^2-1))/(2*x*sqrt(2*x^2-4*x-1));
G.f.: 1/(1+4x-2x^2-x/(1-x/(1+4x-2x^2-x/(1-x/(1+4x-2x^2-x/(1-x/(1-... (continued fraction).
Conjecture: (n+1)*a(n) +2*(2n+1)*a(n-1) +4*(1-n)*a(n-2) +4*(5-2n)*a(n-3) +4*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 17 2011
a(n) ~ (-1)^n * (2 + sqrt(6))^(n+1) / (2^(3/4) * 3^(1/4) * sqrt(Pi*n)). - Vaclav Kotesovec, Aug 15 2018
MATHEMATICA
CoefficientList[Series[(1/(2*x))*(1 - Sqrt[(1-2*x^2)/(1+4*x-2*x^2)]), {x, 0, 50}], x] (* G. C. Greubel, Aug 14 2018 *)
PROG
(PARI) x='x+O('x^50); Vec((1/(2*x))*(1-sqrt((1-2*x^2)/(1+4*x-2*x^2)))) \\ G. C. Greubel, Aug 14 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1/(2*x))*(1-Sqrt((1-2*x^2)/(1+4*x-2*x^2))))); // G. C. Greubel, Aug 14 2018
CROSSREFS
Sequence in context: A077829 A088132 A122450 * A258788 A100389 A151163
KEYWORD
sign,easy
AUTHOR
Paul Barry, Jan 09 2011
STATUS
approved