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 A354310 #13 May 24 2022 08:11:35
%S A354310 1,0,2,9,84,990,14754,264600,5549424,133217784,3601384200,
%T A354310 108249692760,3580724721672,129250420556400,5055196156459344,
%U A354310 212951257371183240,9612027759287831040,462798880374787387200,23675607840207619145664,1282413928716141429168000
%N A354310 Expansion of e.g.f. 1/(1 - 3*x)^(x/3).
%F A354310 a(0) = 1; a(n) = (n-1)! * Sum_{k=2..n} k * 3^(k-2)/(k-1) * a(n-k)/(n-k)!.
%F A354310 a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-2*k) * |Stirling1(n-k,k)|/(n-k)!.
%o A354310 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x)^(x/3)))
%o A354310 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=2, i, j*3^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
%o A354310 (PARI) a(n) = n!*sum(k=0, n\2, 3^(n-2*k)*abs(stirling(n-k, k, 1))/(n-k)!);
%Y A354310 Cf. A066166, A354309.
%Y A354310 Cf. A351735, A354316, A354320.
%K A354310 nonn
%O A354310 0,3
%A A354310 _Seiichi Manyama_, May 23 2022