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 A367888 #10 Apr 29 2025 17:04:20
%S A367888 1,1,4,13,61,304,1747,10945,74830,550687,4335109,36272086,320980645,
%T A367888 2991373597,29253607780,299258487553,3193634980753,35469069928792,
%U A367888 409082335024591,4890313138089133,60489400453642822,772967507343358171,10189818916331129017,138398721137005215526
%N A367888 Expansion of e.g.f. exp(3*(exp(x) - 1) - 2*x).
%F A367888 G.f. A(x) satisfies: A(x) = 1 - x * ( 2 * A(x) - 3 * A(x/(1 - x)) / (1 - x) ).
%F A367888 a(n) = exp(-3) * Sum_{k>=0} 3^k * (k-2)^n / k!.
%F A367888 a(0) = 1; a(n) = -2 * a(n-1) + 3 * Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).
%F A367888 a(n) = Sum_{k=0..n} binomial(n,k) * (-2)^(n-k) * A027710(k).
%p A367888 b:= proc(n, k, m) option remember; `if`(n=0, 3^m, `if`(k>0,
%p A367888 b(n-1, k-1, m+1)*k, 0)+m*b(n-1, k, m)+b(n-1, k+1, m))
%p A367888 end:
%p A367888 a:= n-> b(n, 0$2):
%p A367888 seq(a(n), n=0..23); # _Alois P. Heinz_, Apr 29 2025
%t A367888 nmax = 23; CoefficientList[Series[Exp[3 (Exp[x] - 1) - 2 x], {x, 0, nmax}], x] Range[0, nmax]!
%t A367888 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, 23}]
%t A367888 Table[Sum[Binomial[n, k] (-2)^(n - k) BellB[k, 3], {k, 0, n}], {n, 0, 23}]
%o A367888 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(3*(exp(x) - 1) - 2*x))) \\ _Michel Marcus_, Dec 04 2023
%Y A367888 Cf. A000296, A027710, A126617, A194689, A355254, A367889.
%K A367888 nonn
%O A367888 0,3
%A A367888 _Ilya Gutkovskiy_, Dec 04 2023