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 A345200 #15 Jun 19 2021 05:18:48
%S A345200 1,1,2,5,12,32,84,234,652,1872,5416,15922,47188,141283,425910,1293105,
%T A345200 3948080,12118619,37367694,115708111,359623780,1121543440,3508533500,
%U A345200 11006973980,34620982004,109157354769,344928572562,1092190467567,3464955417200,11012117992012
%N A345200 G.f. A(x) satisfies: A(x) = x + x^2 * exp(2 * Sum_{k>=1} A(x^k) / k).
%F A345200 G.f.: x + x^2 / Product_{n>=1} (1 - x^n)^(2*a(n)).
%F A345200 a(n+2) = (2/n) * Sum_{k=1..n} ( Sum_{d|k} d * a(d) ) * a(n-k+2).
%F A345200 a(n) ~ c * d^n / n^(3/2), where d = 3.3437762102302517833309792925121217026126033230718263962128740290952197... and c = 0.3397354606156870289877990463189432389789387070060129709272911771... - _Vaclav Kotesovec_, Jun 19 2021
%t A345200 nmax = 30; A[_] = 0; Do[A[x_] = x + x^2 Exp[2 Sum[A[x^k]/k, {k, 1, nmax}]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%t A345200 a[1] = a[2] = 1; a[n_] := a[n] = (2/(n - 2)) Sum[Sum[d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 30}]
%Y A345200 Cf. A000151, A007562, A345241, A345242.
%K A345200 nonn
%O A345200 1,3
%A A345200 _Ilya Gutkovskiy_, Jun 11 2021