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 A368237 #13 Dec 18 2023 12:11:45
%S A368237 1,4,31,361,5605,108781,2533447,68836279,2137543177,74673228457,
%T A368237 2898494302651,123757822391083,5764497138070381,290878956151681405,
%U A368237 15806942065094830735,920336494043393536591,57157621592164505969425,3771643127452655490322513
%N A368237 Expansion of e.g.f. 1/(exp(-x) - 3*x).
%F A368237 a(0) = 1; a(n) = 3*n*a(n-1) + Sum_{k=1..n} (-1)^(k-1) * binomial(n,k) * a(n-k).
%F A368237 a(n) = n! * Sum_{k=0..n} 3^(n-k) * (n-k+1)^k / k!.
%t A368237 a[n_] := n! Sum[3^(n - k) (n - k + 1)^k / k!, {k, 0, n}];Table[a[n],{n,0,17}] (* or *) a[0] = 1;a[n_] := 3n a[n - 1] + Sum[(-1)^(k - 1) Binomial[n, k] a[n - k], {k, 1, n}];Table[a[n],{n,0,17}] (* _James C. McMahon_, Dec 18 2023 *)
%o A368237 (PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*(n-k+1)^k/k!);
%o A368237 (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(exp(-x) - 3*x))) \\ _Michel Marcus_, Dec 18 2023
%Y A368237 Cf. A072597, A368236.
%Y A368237 Cf. A336948.
%K A368237 nonn
%O A368237 0,2
%A A368237 _Seiichi Manyama_, Dec 18 2023