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 A349559 #35 Aug 28 2022 04:24:59
%S A349559 1,0,2,3,44,270,3714,44940,746528,13149864,271954440,6154715160,
%T A349559 155055594792,4254730262640,127019898548256,4088313657038520,
%U A349559 141301521555548160,5216698433745207360,204946906542573645504,8536144551987171202560
%N A349559 E.g.f. satisfies A(x) = 1/(1 - x*A(x))^x.
%F A349559 a(n) ~ sqrt(1 + r - 2*r*log(r)) * n^(n-1) / ((1+r)^2 * exp(n) * r^(n + 1/2)), where r = 0.4214518303433019663622598075106479936652984008256... is the root of the equation r^(1-r) * (1+r)^(1+r) = 1. - _Vaclav Kotesovec_, Nov 22 2021
%F A349559 a(n) = n! * Sum_{k=0..floor(n/2)} (n-k+1)^(k-1) * |Stirling1(n-k,k)|/(n-k)!. - _Seiichi Manyama_, Aug 27 2022
%p A349559 a:= n-> n!*coeff(series(RootOf(1/(1-x*A)^x-A, A), x, n+1), x, n):
%p A349559 seq(a(n), n=0..20); # _Alois P. Heinz_, Nov 22 2021
%t A349559 nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 - x*A[x])^x + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Nov 22 2021 *)
%o A349559 (PARI) my(A=1,n=22); for(i=1, n, A=(1-x*A)^(-x+x*O(x^n))); Vec(serlaplace(A))
%o A349559 (PARI) a(n) = n!*sum(k=0, n\2, (n-k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!); \\ _Seiichi Manyama_, Aug 27 2022
%Y A349559 Cf. A007113, A349556.
%Y A349559 Cf. A184949, A356786, A356787.
%K A349559 nonn
%O A349559 0,3
%A A349559 _Seiichi Manyama_, Nov 22 2021