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 A355233 #25 Jun 26 2022 02:58:11
%S A355233 0,1,0,4,6,40,150,832,4494,27496,178278,1240720,9159678,71523448,
%T A355233 588049878,5073746464,45800173038,431400176008,4230061102662,
%U A355233 43087882883248,455079854567646,4975136823055768,56212975652894646,655496634896272960,7878552380411524302
%N A355233 E.g.f. A(x) satisfies A'(x) = 1 + 2 * (exp(x) - 1) * A(x).
%F A355233 a(0) = 0, a(1) = 1; a(n+1) = 2 * Sum_{k=1..n-1} binomial(n,k) * a(k).
%F A355233 From _Vaclav Kotesovec_, Jun 26 2022: (Start)
%F A355233 E.g.f.: 3*exp(2*exp(x) - 2*x - 2)/4 - 1/(exp(2*x)*4) - 1/(2*exp(x)).
%F A355233 a(n) = 3*A194689(n)/4 - (-1)^n * (2^(n-2) + 1/2).
%F A355233 a(n) ~ 3 * n^(n-2) * exp(n/LambertW(n/2) - n - 2) / (sqrt(1 + LambertW(n/2)) * LambertW(n/2)^(n-2)). (End)
%t A355233 nmax = 25; CoefficientList[Series[3*E^(-2 + 2*E^x - 2*x)/4 - 1/(E^(2*x)*4) - 1/(2*E^x), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Jun 25 2022 *)
%o A355233 (PARI) a_vector(n) = my(v=vector(n)); v[1]=1; for(i=1, n-1, v[i+1]=2*sum(j=1, i-1, binomial(i, j)*v[j])); concat(0, v);
%Y A355233 Cf. A004123, A087650, A194689, A355206, A355232.
%K A355233 nonn
%O A355233 0,4
%A A355233 _Seiichi Manyama_, Jun 25 2022
%E A355233 Prepended a(0)=0 from _Vaclav Kotesovec_, Jun 25 2022