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 A192399 #13 Feb 27 2014 01:37:15
%S A192399 1,1,3,11,48,233,1218,6722,38668,229864,1403618,8766186,55818141,
%T A192399 361499355,2376956264,15845876429,106988044753,731026642533,
%U A192399 5051920683481,35296182297157,249249589433312,1778775804736254,12828718640894604
%N A192399 G.f. A(x) satisfies: A(x) = 1 + Sum_{n>=1} x^n * A(x)^n/(1 - x*A(x)^(2*n)).
%C A192399 Related q-series identity:
%C A192399 Sum_{n>=1} z^n*y*q^n/(1-y*q^(2*n)) = Sum_{n>=1} y^n*z*q^(2*n-1)/(1-z*q^(2*n-1)); here q=A(x), y=x, z=x.
%F A192399 G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^(2*n-1)/(1 - x*A(x)^(2*n-1)).
%F A192399 G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^(n*(n+1)/2) * Sum_{k=0..n-1} A(x)^(-k*(k+1)/2). - _Paul D. Hanna_, Jul 01 2011
%e A192399 G.f.: A(x) = 1 + x + 3*x^2 + 11*x^3 + 48*x^4 + 233*x^5 + 1218*x^6 +...
%e A192399 which satisfies the following relations:
%e A192399 A(x) = 1 + x*A(x)/(1-x*A(x)^2) + x^2*A(x)^2/(1-x*A(x)^4) + x^3*A(x)^3/(1-x*A(x)^6) +...
%e A192399 A(x) = 1 + x*A(x)/(1-x*A(x)) + x^2*A(x)^3/(1-x*A(x)^3) + x^3*A(x)^5/(1-x*A(x)^5) +...
%e A192399 A(x) = 1 + x*A(x) + x^2*A(x)^3*(1 + 1/A(x)) + x^3*A(x)^6*(1 + 1/A(x) + 1/A(x)^3) + x^4*A(x)^10*(1 + 1/A(x) + 1/A(x)^3 + 1/A(x)^6) +...
%o A192399 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*A^m/(1-x*A^(2*m)+x*O(x^n))));polcoeff(A,n)}
%o A192399 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*A^(2*m-1)/(1-x*A^(2*m-1)+x*O(x^n))));polcoeff(A,n)}
%o A192399 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*A^(m*(m+1)/2)*sum(k=0,m-1,(A+x*O(x^n))^(-k*(k+1)/2) ) ) );polcoeff(A,n)}
%Y A192399 Cf. A192400, A192401, A192405.
%K A192399 nonn
%O A192399 0,3
%A A192399 _Paul D. Hanna_, Jun 30 2011