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 A363385 #7 May 30 2023 19:39:01
%S A363385 1,1,0,1,2,2,4,11,14,29,66,115,222,493,944,1884,4020,8175,16618,35198,
%T A363385 73220,151844,321036,676778,1421828,3016813,6407344,13589888,28962702,
%U A363385 61853827,132073646,282752030,606492428,1301587833,2797816706,6023460551,12978238202,27995493484
%N A363385 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} A(x^k)^2 / k ).
%t A363385 nmax = 38; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[A[x^k]^2/k, {k, 1, nmax}]] + O[x]^(nmax + 1)//Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%t A363385 a[1] = a[2] = 1; g[n_] := g[n] = Sum[a[k] a[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[d g[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 38}]
%o A363385 (PARI) seq(n)=my(p=x+x^2+O(x^3)); for(n=1, n\2, my(m=serprec(p,x)-1); p = x + x^2*exp(sum(k=1, m\2, subst(p + O(x^(m\k+1)), x, x^k)^2/k))); Vec(p + O(x*x^n)) \\ _Andrew Howroyd_, May 30 2023
%Y A363385 Cf. A005750, A007562, A363386.
%K A363385 nonn
%O A363385 1,5
%A A363385 _Ilya Gutkovskiy_, May 30 2023