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 A353222 #20 May 04 2022 05:00:50
%S A353222 1,0,2,0,12,60,120,2520,15120,90720,1693440,13305600,140374080,
%T A353222 2724321600,27744837120,414096883200,8689288608000,111399326438400,
%U A353222 2114134793971200,48501156601497600,759659036405068800,17279306372135808000,434100706059205785600
%N A353222 Expansion of e.g.f. (1 - x^3)^(-1/x).
%F A353222 a(0) = 1; a(n) = (n-1)! * Sum_{k=1..floor((n+1)/3)} (3*k-1)/k * a(n-3*k+1)/(n-3*k+1)!.
%F A353222 a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (3*exp(n)). - _Vaclav Kotesovec_, May 04 2022
%o A353222 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^3)^(-1/x)))
%o A353222 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-log(1-x^3)/x)))
%o A353222 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, (i+1)\3, (3*j-1)/j*v[i-3*j+2]/(i-3*j+1)!)); v;
%Y A353222 Cf. A121452, A353224.
%Y A353222 Cf. A246689, A353223.
%K A353222 nonn
%O A353222 0,3
%A A353222 _Seiichi Manyama_, May 01 2022