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 A353223 #22 May 04 2022 05:03:00
%S A353223 1,1,1,1,13,61,181,2101,19321,107353,1338121,18021961,153519301,
%T A353223 2162889301,37434929533,437750929981,7054260835441,146656527486001,
%U A353223 2197288472426641,40414798347009553,970905798377330941,17791752518018762221,370864149434372540101
%N A353223 Expansion of e.g.f. (1 - x^3)^(-1/x^2).
%F A353223 a(0) = 1; a(n) = (n-1)! * Sum_{k=1..floor((n+2)/3)} (3*k-2)/k * a(n-3*k+2)/(n-3*k+2)!.
%F A353223 a(n) = n! * Sum_{k=0..floor(n/3)} |Stirling1(n-2*k,n-3*k)|/(n-2*k)!.
%F A353223 a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (3*exp(n)). - _Vaclav Kotesovec_, May 04 2022
%o A353223 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^3)^(-1/x^2)))
%o A353223 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-log(1-x^3)/x^2)))
%o A353223 (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+2)\3, (3*j-2)/j*v[i-3*j+3]/(i-3*j+2)!)); v;
%o A353223 (PARI) a(n) = n!*sum(k=0, n\3, abs(stirling(n-2*k, n-3*k, 1))/(n-2*k)!);
%Y A353223 Cf. A121452, A246689, A353222, A353225.
%K A353223 nonn
%O A353223 0,5
%A A353223 _Seiichi Manyama_, May 01 2022