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 A354316 #12 Mar 06 2023 13:16:16
%S A354316 1,0,2,9,96,1170,18324,340200,7360128,181476288,5024611440,
%T A354316 154319988240,5206240427904,191372822989920,7612497915813504,
%U A354316 325791049256094240,14925809593280332800,728828735500650355200,37786217117138333005824
%N A354316 Expansion of e.g.f. 1/(1 + x/3 * log(1 - 3 * x)).
%F A354316 a(0) = 1; a(n) = n! * Sum_{k=2..n} 3^(k-2)/(k-1) * a(n-k)/(n-k)!.
%F A354316 a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-2*k) * k! * |Stirling1(n-k,k)|/(n-k)!.
%t A354316 With[{nn=20},CoefficientList[Series[1/(1+x/3 Log[1-3x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 06 2023 *)
%o A354316 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x/3*log(1-3*x))))
%o A354316 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=2, i, 3^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
%o A354316 (PARI) a(n) = n!*sum(k=0, n\2, 3^(n-2*k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);
%Y A354316 Cf. A052830, A354315.
%Y A354316 Cf. A354310.
%K A354316 nonn
%O A354316 0,3
%A A354316 _Seiichi Manyama_, May 23 2022