This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A196865 #8 Mar 30 2012 18:37:31
%S A196865 1,3,18,-117,-1971,16119,343278,-3036528,-71818164,661017348,
%T A196865 16593480504,-156436510221,-4080815440497,39095628518637,
%U A196865 1047594828442626,-10152600834566916,-277489726161424569,2712640349690579349,75279129630178436622,-740885355955719640809
%N A196865 G.f. A(x) satisfies: A(x)^-3 + A(-x)^-3 = 2 and A(x)^3 - A(-x)^3 = 18*x.
%F A196865 G.f.: ( (sqrt(1+4*3^4*x^2) + 2*3^2*x)*(sqrt(1+4*3^4*x^2) + 1)/2 )^(1/6).
%e A196865 G.f.: A(x) = 1 + 3*x + 18*x^2 - 117*x^3 - 1971*x^4 + 16119*x^5 +...
%e A196865 where
%e A196865 A(x)^3 = 1 + 9*x + 81*x^2 - 6561*x^4 + 1062882*x^6 - 215233605*x^8 +...
%e A196865 A(x)^-3 = 1 - 9*x + 729*x^3 - 118098*x^5 + 23914845*x^7 - 5423886846*x^9 +...
%o A196865 (PARI) {a(n)=local(A=[1,3]);for(k=2,n,A=concat(A,0);if(k%2==1,A[#A]=-Vec(Ser(A)^3)[#A]/3,A[#A]=Vec(Ser(A)^-3)[#A]/3));A[n+1]}
%o A196865 (PARI) {a(n)=local(X=x+x*O(x^n));polcoeff(((sqrt(1+4*3^4*X^2) + 2*3^2*x)*(sqrt(1+4*3^4*X^2) + 1)/2 )^(1/6),n)}
%Y A196865 Cf. A196864, A193618, A193619, A196866, A196867, A196868, A196869.
%K A196865 sign
%O A196865 0,2
%A A196865 _Paul D. Hanna_, Oct 06 2011