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A059279 G.f. is ((1-x)/(1-2*x)) * G(x*(1-x)/(1-2*x)) where G(x) is g.f. for Catalan numbers A000108. 2
1, 2, 6, 20, 72, 276, 1112, 4656, 20080, 88608, 398144, 1815248, 8375904, 39037120, 183493440, 868853120, 4140414720, 19841656960, 95559048960, 462268075520, 2245165391360, 10943794652160, 53519094753280, 262510076263680, 1291131867203072 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is A134751. Binomial transform of A105864. [From Paul Barry, Oct 07 2008]

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

Conjecture: (n+1)*a(n) +2*(1-4*n)*a(n-1) + 4*(4*n-5)*a(n-2) +4*(5-2*n)*a(n-3)=0. - R. J. Mathar, Nov 15 2011

G.f.: (1 - sqrt(1 - 4*x*(1 - x)/(1 - 2*x)))/(2*x). - G. C. Greubel, Jan 04 2017

G.f. A(x) satisfies: A(x) = 1 + x * (1/(1 - 2*x) + A(x)^2). - Ilya Gutkovskiy, Jun 30 2020

a(n) ~ 5^(1/4) * 2^(n-1) * phi^(2*n + 3/2) / (sqrt(Pi) * n^(3/2)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 30 2020

MATHEMATICA

CoefficientList[Series[(1 - Sqrt[1 - 4*t*(1 - t)/(1 - 2*t)])/(2*t), {t, 0, 50}], t] (* G. C. Greubel, Jan 04 2017 *)

PROG

(PARI) Vec((1 - sqrt(1 - 4*t*(1 - t)/(1 - 2*t)))/(2*t) + O(t^50)) \\ G. C. Greubel, Jan 04 2017

CROSSREFS

Sequence in context: A122737 A338184 A150134 * A154381 A150135 A150136

Adjacent sequences:  A059276 A059277 A059278 * A059280 A059281 A059282

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 24 2001

STATUS

approved

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Last modified June 18 17:29 EDT 2021. Contains 345120 sequences. (Running on oeis4.)