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A085403
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Expansion of (1-x+sqrt(1-6x+x^2))/2 in powers of x.
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10
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1, -2, -2, -6, -22, -90, -394, -1806, -8558, -41586, -206098, -1037718, -5293446, -27297738, -142078746, -745387038, -3937603038, -20927156706, -111818026018, -600318853926, -3236724317174, -17518619320890, -95149655201962, -518431875418926, -2832923350929742
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OFFSET
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0,2
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COMMENTS
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Series reversion of x(Sum_{k>=0} a(k)x^k) is x(Sum_{k>=0} A027307(k)x^k).
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LINKS
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FORMULA
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G.f.: (1-x+sqrt(1-6x+x^2))/2. (=1/g.f. A006318)
Given g.f. A(x), y=A(x)x satisfies 0=f(x, y) where f(x, y)=y(y-x)+(x+y)x^2 . - Michael Somos, May 23 2005
G.f.: Q(0) where Q(k) = 1 + k*(1-x) - x - x*(k+1)*(k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Mar 14 2013
a(n) ~ -sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^n / (2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 20 2014
D-finite with recurrence: n*a(n) +3*(-2*n+3)*a(n-1) +(n-3)*a(n-2)=0. - R. J. Mathar, Jan 20 2020
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MATHEMATICA
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CoefficientList[Series[(1-x+Sqrt[1-6x+x^2])/2, {x, 0, 30}], x] (* Harvey P. Dale, Jun 13 2013 *)
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PROG
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(PARI) a(n)=polcoeff((1-x+sqrt(1-6*x+x^2+x*O(x^n)))/2, n)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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