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.
{a(n)=local(A=1+x+x*O(x^n),B);for(n=0,n,B=serreverse(x/A^6);A=1/(1-B));polcoeff(A,n)}
{a(n)=local(A=1+x+x*O(x^n),B);for(n=0,n,B=serreverse(x/A^2);A=1/(1-B)^3);polcoeff(A,n)}
A[0]:= x -> 1+c*x: for n from 1 to 20 do cc:= coeff(series(A[n-1](x/A[n-1](x))-1/(1-x)^6, x, n+1),x,n); A[n]:= unapply(eval(A[n-1](x),c=solve(cc,c))+c*x^(n+1),x); od: seq(coeff(A[20](x),x,j),j=0..20); # Robert Israel, Aug 19 2018
nmax = 16; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[A[x/A[x]] - 1/(1 - x)^6 + O[x]^(n + 1), x] == 0 /. sol; sol = sol ~Join~ Solve[eq] [[1]], {n, 1, nmax}]; sol /. Rule -> Set;
a /@ Range[0, nmax] (* Jean-François Alcover, Nov 01 2019 *)
{a(n)=local(A=1+x+x*O(x^n),B);for(n=0,n,B=serreverse(x/A);A=1/(1-B)^6);polcoeff(A,n)}