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%I #22 Jan 30 2020 21:29:15
%S 1,-2,-2,-6,-22,-90,-394,-1806,-8558,-41586,-206098,-1037718,-5293446,
%T -27297738,-142078746,-745387038,-3937603038,-20927156706,
%U -111818026018,-600318853926,-3236724317174,-17518619320890,-95149655201962,-518431875418926,-2832923350929742
%N Expansion of (1-x+sqrt(1-6x+x^2))/2 in powers of x.
%C Series reversion of x(Sum_{k>=0} a(k)x^k) is x(Sum_{k>=0} A027307(k)x^k).
%H Vincenzo Librandi, <a href="/A085403/b085403.txt">Table of n, a(n) for n = 0..200</a>
%F G.f.: (1-x+sqrt(1-6x+x^2))/2. (=1/g.f. A006318)
%F 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
%F 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
%F a(n) ~ -sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^n / (2*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Apr 20 2014
%F 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
%t CoefficientList[Series[(1-x+Sqrt[1-6x+x^2])/2,{x,0,30}],x] (* _Harvey P. Dale_, Jun 13 2013 *)
%o (PARI) a(n)=polcoeff((1-x+sqrt(1-6*x+x^2+x*O(x^n)))/2,n)
%Y A minor variation of A006318. a(n)=-A006318(n-1), n>1.
%K sign
%O 0,2
%A _Michael Somos_, Jun 28 2003
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