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.
3.9561842030261697545408021818783008332999988095...
G.f.: A(x) = 1 + 2*x + 6*x^2 + 16*x^3 + 154*x^4 + 4584*x^5 + 130464*x^6 + 3816304*x^7 + 123180090*x^8 + 4422532004*x^9 + 175136909492*x^10 + ... such that A = A(x) satisfies A(x) = 1/(2 - A) + ((1+x)^2 - A)/(2 - (1+x)*A)^2 + ((1+x)^3 - A)^2/(2 - (1+x)^2*A)^3 + ((1+x)^4 - A)^3/(2 - (1+x)^3*A)^4 + ((1+x)^5 - A)^4/(2 - (1+x)^4*A)^5 + ((1+x)^6 - A)^5/(2 - (1+x)^5*A)^6 + ... Also, A(x) = 1/(2 + A) + ((1+x)^2 + A)/(2 + (1+x)*A)^2 + ((1+x)^3 + A)^2/(2 + (1+x)^2*A)^3 + ((1+x)^4 + A)^3/(2 + (1+x)^3*A)^4 + ((1+x)^5 + A)^4/(2 + (1+x)^4*A)^5 + ((1+x)^6 + A)^5/(2 + (1+x)^5*A)^6 + ...
{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0); A = Vec( sum(m=0,#A, ( (1+x)^(m+1) - Ser(A) )^m / (2 - (1+x)^m*Ser(A))^(m+1) ) ) ); A[n+1]}
for(n=0,30,print1(a(n),", "))
E.g.f.: A(x) = 1 + x + 5*x^2/2! + 85*x^3/3! + 5261*x^4/4! + 549061*x^5/5! + 79707245*x^6/6! + 15531175045*x^7/7! + 3926159465261*x^8/8! + 1249497583485061*x^9/9! + ... such that A = A(x) satisfies A(x) = 1/(2 - A) + (exp(x) - A)/(2 - exp(x)*A)^2 + (exp(2*x) - A)^2/(2 - exp(2*x)*A)^3 + (exp(3*x) - A)^3/(2 - exp(3*x)*A)^4 + (exp(4*x) - A)^4/(2 - exp(4*x)*A)^5 + (exp(5*x) - A)^5/(2 - exp(5*x)*A)^6 + ... Also, A(x) = 1/(2 + A) + (exp(x) + A)/(2 + exp(x)*A)^2 + (exp(2*x) + A)^2/(2 + exp(2*x)*A)^3 + (exp(3*x) + A)^3/(2 + exp(3*x)*A)^4 + (exp(4*x) + A)^4/(2 + exp(4*x)*A)^5 + (exp(5*x) + A)^5/(2 + exp(5*x)*A)^6 + ...
{a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A = Vec( sum(m=0, #A, ( exp(m*x +x*O(x^#A)) - Ser(A) )^m / (2 - exp(m*x +x*O(x^#A))*Ser(A))^(m+1) ) ) ); n!*A[n+1]}
for(n=0, 20, print1(a(n), ", "))
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