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%I #7 Mar 30 2012 18:37:31
%S 1,6,-36,216,-2592,23328,-311040,3265920,-45349632,517321728,
%T -7336562688,88159684608,-1266403590144,15771513618432,
%U -228509902503936,2921050338066432,-42583086769766400,555279063084564480,-8132204141176946688,107718176292801085440
%N G.f. A(x) satisfies: A(x)^3 + A(-x)^3 = 2 and A(x)^2 - A(-x)^2 = 24*x.
%e G.f.: A(x) = 1 + 6*x - 36*x^2 + 216*x^3 - 2592*x^4 + 23328*x^5 +...
%e where
%e A(x)^2 = 1 + 12*x - 36*x^2 - 1296*x^4 - 108864*x^6 - 12317184*x^8 +...
%e A(x)^3 = 1 + 18*x - 432*x^3 - 23328*x^5 - 2239488*x^7 - 272097792*x^9 +...
%o (PARI) {a(n)=local(A=[1,6]);for(k=2,n,A=concat(A,0);if(k%2==1,A[#A]=-Vec(Ser(A)^2)[#A]/2,A[#A]=-Vec(Ser(A)^3)[#A]/3));A[n+1]}
%Y Cf. A196868, A193618, A193619, A196864, A196865, A196866, A196867.
%K sign
%O 0,2
%A _Paul D. Hanna_, Oct 06 2011
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