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 A367785 #7 Dec 01 2023 15:59:08
%S A367785 1,2,13,89,772,7745,87949,1109288,15332539,229840361,3706130914,
%T A367785 63857565095,1169261937973,22646779177898,462143532144937,
%U A367785 9902312863237637,222119823632283628,5202170552214520637,126914730275907871201,3218552632981994910248,84686139239808135094879,2307953474037054591248501
%N A367785 Expansion of e.g.f. exp(exp(3*x) - x - 1).
%F A367785 a(n) = exp(-1) * Sum_{k>=0} (3*k-1)^n / k!.
%F A367785 a(0) = 1; a(n) = -a(n-1) + Sum_{k=1..n} binomial(n-1,k-1) * 3^k * a(n-k).
%F A367785 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * 3^k * Bell(k).
%t A367785 nmax = 21; CoefficientList[Series[Exp[Exp[3 x] - x - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t A367785 a[0] = 1; a[n_] := a[n] = -a[n - 1] + Sum[Binomial[n - 1, k - 1] 3^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]
%t A367785 Table[Sum[(-1)^(n - k) Binomial[n, k] 3^k BellB[k], {k, 0, n}], {n, 0, 21}]
%o A367785 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(exp(3*x) - x - 1))) \\ _Michel Marcus_, Nov 30 2023
%Y A367785 Cf. A000110, A000296, A124311, A247452, A284859, A284860, A330605, A367744, A367786.
%K A367785 nonn
%O A367785 0,2
%A A367785 _Ilya Gutkovskiy_, Nov 30 2023