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 A347666 #4 Sep 10 2021 19:22:52
%S A347666 1,2,8,40,239,1648,12778,109476,1023520,10341878,112067820,1294254184,
%T A347666 15847382977,204827368606,2784056034014,39665514607872,
%U A347666 590684848605779,9170941154737032,148120725648168260,2483657480026985432,43157660169344697996,775898068395820783674
%N A347666 E.g.f.: exp( exp(x) * (1 + x + x^2 / 2 + x^3 / 6) - 1 ).
%C A347666 Exponential transform of A000125.
%F A347666 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A000125(k) * a(n-k).
%t A347666 nmax = 21; CoefficientList[Series[Exp[Exp[x] (1 + x + x^2/2 + x^3/6) - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t A347666 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] ((k^3 + 5 k + 6)/6) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]
%Y A347666 Cf. A000125, A001680, A209801, A347665.
%K A347666 nonn
%O A347666 0,2
%A A347666 _Ilya Gutkovskiy_, Sep 10 2021