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A098477 Expansion of 1/sqrt(1-2*x-7*x^2+8*x^3). 2
1, 1, 5, 9, 37, 89, 325, 905, 3109, 9337, 31173, 97449, 321445, 1027225, 3374405, 10920649, 35855909, 116937145, 384340421, 1259728873, 4147000229, 13639616473, 44978045765, 148314302473, 489879442469, 1618600915705 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

1/sqrt(1-2*x-(4*r-1)*x^2+4*r^3) expands to give Sum_{k=0..floor(n/2)} binomial(2*k,k)*binomial(n-k,n-2*k)*r^k.

LINKS

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

FORMULA

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

G.f.: 1/(1-x-4x^2/(1-0x-2x^2/(1-x-2x^2/(1-0x-2x^2/(1-x-2x^2/.... (continued fraction). - Paul Barry, Dec 07 2008

D-finite: n*a(n) +(1-2*n)*a(n-1) +7*(1-n)*a(n-2) +4*(2*n-3)*a(n-3)=0. - R. J. Mathar, Nov 09 2012

a(n) ~ 16 * ((1+sqrt(33))/2)^n / (sqrt(594-50*sqrt(33)) * sqrt(Pi*n)). - Vaclav Kotesovec, Feb 04 2014

MATHEMATICA

CoefficientList[Series[1/Sqrt[1-2*x-7*x^2+8*x^3], {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 04 2014 *)

PROG

(PARI) x='x+O('x^50); Vec(1/sqrt(1-2*x-7*x^2+8*x^3)) \\ G. C. Greubel, Mar 16 2017

CROSSREFS

Cf. A026569, A098478.

Sequence in context: A083832 A070969 A200376 * A243762 A303801 A304849

Adjacent sequences:  A098474 A098475 A098476 * A098478 A098479 A098480

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 10 2004

STATUS

approved

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Last modified January 28 13:05 EST 2020. Contains 331321 sequences. (Running on oeis4.)