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 A363388 #6 May 30 2023 19:53:09
%S A363388 1,1,1,2,5,10,28,70,190,517,1441,4057,11572,33294,96620,282319,830178,
%T A363388 2454384,7292106,21759413,65185967,195976025,591097127,1788122219,
%U A363388 5423917828,16493458475,50270190728,153544874713,469916030995,1440807810639,4425266768759,13613578089594,41943137192265
%N A363388 G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^2 / (k*x^k) ).
%t A363388 nmax = 33; A[_] = 0; Do[A[x_] = x + x^2 Exp[Sum[(-1)^(k + 1) A[x^k]^2/(k x^k), {k, 1, nmax}]] + O[x]^(nmax + 1)//Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%t A363388 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[(-1)^(k/d + 1) d g[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 33}]
%o A363388 (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, (-1)^k*subst(p + O(x^(m\k+1)), x, x^k)^2/(x^k*k)))); Vec(p + O(x*x^n)) \\ _Andrew Howroyd_, May 30 2023
%Y A363388 Cf. A005754, A007560, A363387.
%K A363388 nonn
%O A363388 1,4
%A A363388 _Ilya Gutkovskiy_, May 30 2023