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A245924
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Expansion of (1-x - sqrt(1 - 14*x + x^2)) / (6*x*(1 - 14*x + x^2)).
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3
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1, 18, 279, 4132, 59949, 860022, 12252547, 173756232, 2456093529, 34634926810, 487525847535, 6852798238572, 96216461002117, 1349689029354558, 18918661407653979, 265016591806251664, 3710426585319049905, 51924984423522889122, 726369947645489367751, 10157588028419864394420
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OFFSET
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0,2
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COMMENTS
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Limit a(n+1)/a(n) = 7 + 4*sqrt(3).
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LINKS
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FORMULA
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a(n) ~ (26 + 15*sqrt(3)) * (7 + 4*sqrt(3))^n / 24 * (1 - 1/(3^(1/4)*sqrt(Pi*n/2))). - Vaclav Kotesovec, Aug 17 2014
D-finite with recurrence: (n+1)*a(n) +7*(-4*n-1)*a(n-1) +99*(2*n-1)*a(n-2) +7*(-4*n+5)*a(n-3) +(n-2)*a(n-4)=0. - R. J. Mathar, Jan 23 2020
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EXAMPLE
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G.f.: A(x) = 1 + 18*x + 279*x^2 + 4132*x^3 + 59949*x^4 + 860022*x^5 +...
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MATHEMATICA
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CoefficientList[Series[(1 - x - Sqrt[1 - 14*x + x^2])/(6*x*(1 - 14*x + x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 14 2017 *)
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PROG
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(PARI) {a(n)=polcoeff( (1-x - sqrt(1-14*x+x^2 +x^2*O(x^n))) / (6*x*(1-14*x+x^2 +x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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