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 A367889 #7 Dec 05 2023 04:23:34
%S A367889 1,5,28,173,1165,8468,65923,546197,4791214,44301143,430158397,
%T A367889 4372004546,46381674085,512328076385,5879362011436,69958289731457,
%U A367889 861605015493073,10965899141265500,144018319806024991,1949190279770578145,27153595018237222774
%N A367889 Expansion of e.g.f. exp(3*(exp(x) - 1) + 2*x).
%F A367889 G.f. A(x) satisfies: A(x) = 1 + x * ( 2 * A(x) + 3 * A(x/(1 - x)) / (1 - x) ).
%F A367889 a(n) = exp(-3) * Sum_{k>=0} 3^k * (k+2)^n / k!.
%F A367889 a(0) = 1; a(n) = 2 * a(n-1) + 3 * Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).
%F A367889 a(n) = Sum_{k=0..n} binomial(n,k) * 2^(n-k) * A027710(k).
%t A367889 nmax = 20; CoefficientList[Series[Exp[3 (Exp[x] - 1) + 2 x], {x, 0, nmax}], x] Range[0, nmax]!
%t A367889 a[0] = 1; a[n_] := a[n] = 2 a[n - 1] + 3 Sum[Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
%t A367889 Table[Sum[Binomial[n, k] 2^(n - k) BellB[k, 3], {k, 0, n}], {n, 0, 20}]
%o A367889 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(3*(exp(x) - 1) + 2*x))) \\ _Michel Marcus_, Dec 04 2023
%Y A367889 Cf. A000110, A005493, A035009, A078940, A355247, A367888.
%K A367889 nonn
%O A367889 0,2
%A A367889 _Ilya Gutkovskiy_, Dec 04 2023