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 A355284 #8 Jul 01 2022 04:09:27
%S A355284 1,0,0,2,6,24,200,1560,12936,130368,1458432,17623440,233922480,
%T A355284 3376625472,52382131776,870882440064,15459372915840,291596692838400,
%U A355284 5824039155720192,122814724467223296,2726547887891407104,63562453551393223680,1552499303360183700480
%N A355284 Expansion of e.g.f. 1 / (1 + x + x^2/2 + log(1 - x)).
%F A355284 E.g.f.: 1 / (1 - Sum_{k>=3} x^k/k).
%F A355284 a(0) = 1; a(n) = Sum_{k=3..n} binomial(n,k) * (k-1)! * a(n-k).
%t A355284 nmax = 22; CoefficientList[Series[1/(1 + x + x^2/2 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A355284 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (k - 1)! a[n - k], {k, 3, n}]; Table[a[n], {n, 0, 22}]
%o A355284 (PARI) my(x='x+O('x^30)); Vec(serlaplace(1/(1 + x + x^2/2 + log(1 - x)))) \\ _Michel Marcus_, Jun 27 2022
%Y A355284 Cf. A007840, A038205, A102233, A226226, A355285.
%K A355284 nonn
%O A355284 0,4
%A A355284 _Ilya Gutkovskiy_, Jun 26 2022