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 A358081 #21 Aug 12 2025 12:37:27
%S A358081 1,0,0,6,24,60,840,10290,80976,847224,13306320,190271070,2677088040,
%T A358081 46082426676,874515884424,16582066303530,336875275380000,
%U A358081 7539189088358640,176554878235711776,4295134487197296054,111114287924643309240,3036073975138066955820
%N A358081 Expansion of e.g.f. 1/(1 - x^3 * exp(x)).
%H A358081 Seiichi Manyama, <a href="/A358081/b358081.txt">Table of n, a(n) for n = 0..431</a>
%F A358081 a(n) = n! * Sum_{k=0..floor(n/3)} k^(n - 3*k)/(n - 3*k)!.
%F A358081 a(n) ~ n! / ((1 + LambertW(1/3)) * 3^(n+1) * LambertW(1/3)^n). - _Vaclav Kotesovec_, Oct 30 2022
%t A358081 With[{nn=30},CoefficientList[Series[1/(1-x^3 Exp[x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 12 2025 *)
%o A358081 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3*exp(x))))
%o A358081 (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)/(n-3*k)!);
%Y A358081 Cf. A006153, A358080.
%Y A358081 Cf. A292889, A355575, A358065.
%K A358081 nonn,easy
%O A358081 0,4
%A A358081 _Seiichi Manyama_, Oct 30 2022