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.
nmax = 26; A[] = 0; Do[A[x] = x + x A[A[-x]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
G.f.: A(x) = x + 3*x^2 + 54*x^3 + 3402*x^4 + 618921*x^5 +... A(A(x)) = x + 6*x^2 + 126*x^3 + 7641*x^4 + 1310256*x^5 +...+ a(n)*x^n/3^(n-1) +... As a formal series involving products of iterations of the g.f., A(x) = x + x*A(3x) + x*A(3x)*A(3A(3x)) + x*A(3x)*A(3A(3x))*A(3A(3A(3x))) +... which, upon replacing x with A(3x), yields: A(A(3x)) = A(3x) + A(3x)*A(3A(3x)) + A(3x)*A(3A(3x))*A(3A(3A(3x))) +... thus A(x) = x + x*A(A(3x)).
{a(n,q=3)=local(A=x+x^2);for(i=1,n,A=x+x*subst(A,x,subst(A,x,q*x+O(x^n))));polcoeff(A,n)}
G.f.: A(x) = x + x^2/3 + 2*x^3/3^3 + 10*x^4/3^6 + 137*x^5/3^10 + 5296*x^6/3^15 +...+ a(n)*x^n/3^(n(n-1)/2) +... A(x) = x + x*A(x/3) + x*A(x/3)*A(A(x/3)/3) + x*A(x/3)*A(A(x/3)/3)*A(A(A(x/3)/3)/3) +... A(A(x)) = x + 2*x^2/3 + 10*x^3/3^3 + 137*x^4/3^6 + 5296*x^5/3^10 +... SUMS OF SERIES at certain arguments. A(1) = 1.423879975541542344910599787693637973194... A(1/3) = 0.373293286580877833612329400906044642790... A(A(1/3)) = A(1) - 1 = 0.42387997554... A(A(1)) = 2.387414460111728675082753594461076041830... A(3) = 3 + 3*A(A(1)) = 10.16224338033518602524826...
{a(n)=local(A=x+x^2);for(i=1,n,A=x+x*subst(A,x,subst(A,x,x/3+O(x^n))));3^(n*(n-1)/2)*polcoeff(A,n)}
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