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 A367890 #9 Dec 05 2023 04:25:05
%S A367890 1,0,3,3,30,93,633,3342,22809,156063,1183872,9453711,80455125,
%T A367890 721576560,6809391111,67332650007,695777512638,7493572404345,
%U A367890 83926492573341,975467527353750,11744536832206149,146234590864310019,1880198749437144456,24928860500681953683
%N A367890 Expansion of e.g.f. exp(3*(exp(x) - 1 - x)).
%F A367890 G.f. A(x) satisfies: A(x) = 1 - 3 * x * ( A(x) - A(x/(1 - x)) / (1 - x) ).
%F A367890 a(n) = exp(-3) * Sum_{k>=0} 3^k * (k-3)^n / k!.
%F A367890 a(0) = 1; a(n) = 3 * Sum_{k=1..n-1} binomial(n-1,k) * a(n-k-1).
%F A367890 a(n) = Sum_{k=0..n} binomial(n,k) * (-3)^(n-k) * A027710(k).
%t A367890 nmax = 23; CoefficientList[Series[Exp[3 (Exp[x] - 1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
%t A367890 a[0] = 1; a[n_] := a[n] = 3 Sum[Binomial[n - 1, k] a[n - k - 1], {k, 1, n - 1}]; Table[a[n], {n, 0, 23}]
%t A367890 Table[Sum[Binomial[n, k] (-3)^(n - k) BellB[k, 3], {k, 0, n}], {n, 0, 23}]
%o A367890 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(3*(exp(x) - 1 - x)))) \\ _Michel Marcus_, Dec 04 2023
%Y A367890 Cf. A000296, A027710, A194689, A346738, A355253, A355254, A367888, A367891.
%K A367890 nonn
%O A367890 0,3
%A A367890 _Ilya Gutkovskiy_, Dec 04 2023