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%I #7 Mar 30 2012 18:37:31
%S 1,3,-9,-198,1188,30213,-220239,-5945238,47541735,1325876283,
%T -11192990913,-318640183182,2787445591416,80483342059224,
%U -722019579525288,-21063846331387728,192542324985927324,5661585516173303268,-52508399485861250604,-1553593208517770295816
%N G.f. A(x) satisfies: A(x)^3 + A(-x)^3 = 2 and A(x)^-3 - A(-x)^-3 = -18*x.
%F G.f.: ( 2*(sqrt(1+4*3^4*x^2) + 2*3^2*x)/(sqrt(1+4*3^4*x^2) + 1) )^(1/6).
%e G.f.: A(x) = 1 + 3*x - 9*x^2 - 198*x^3 + 1188*x^4 + 30213*x^5 +...
%e where
%e A(x)^3 = 1 + 9*x - 729*x^3 + 118098*x^5 - 23914845*x^7 + 5423886846*x^9 +...
%e A(x)^-3 = 1 - 9*x + 81*x^2 - 6561*x^4 + 1062882*x^6 - 215233605*x^8 +...
%o (PARI) {a(n)=local(A=[1,3]);for(k=2,n,A=concat(A,0);if(k%2==0,A[#A]=-Vec(Ser(A)^3)[#A]/3,A[#A]=Vec(Ser(A)^-3)[#A]/3));A[n+1]}
%o (PARI) {a(n)=local(X=x+x*O(x^n));polcoeff((2*(sqrt(1+4*3^4*X^2) + 2*3^2*x)/(sqrt(1+4*3^4*X^2) + 1) )^(1/6),n)}
%Y Cf. A196865, A193618, A193619, A196866, A196867, A196868, A196869.
%K sign
%O 0,2
%A _Paul D. Hanna_, Oct 06 2011
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