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 A343686 #8 Apr 26 2021 12:19:18
%S A343686 1,4,33,410,6796,140824,3501782,101589732,3368237928,125634319104,
%T A343686 5206805098752,237370661584704,11805144854303760,636030155604374400,
%U A343686 36903603627294958416,2294156656214759133024,152126925169297299197184,10718105879980375520103936,799564645068022035991527552
%N A343686 a(0) = 1; a(n) = 3 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
%F A343686 E.g.f.: 1 / (1 - 3*x + log(1 - x)).
%F A343686 a(n) ~ n! / ((3/c + 2 - c) * (1 - c/3)^n), where c = LambertW(3*exp(2)) = 2.2761339297716461777892556270138... - _Vaclav Kotesovec_, Apr 26 2021
%t A343686 a[0] = 1; a[n_] := a[n] = 3 n a[n - 1] + Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
%t A343686 nmax = 18; CoefficientList[Series[1/(1 - 3 x + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
%Y A343686 Cf. A007840, A052820, A053486, A343685, A343687.
%K A343686 nonn
%O A343686 0,2
%A A343686 _Ilya Gutkovskiy_, Apr 26 2021