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 A368177 #14 Mar 11 2024 05:05:54
%S A368177 0,1,7,47,402,4569,65298,1119789,22397112,511972065,13166163630,
%T A368177 376208954109,11824734538620,405454640476833,15061050695642994,
%U A368177 602494304797738845,25823425094211472272,1180601869774944168513,57348495330075309426390
%N A368177 Expansion of e.g.f. -log(1 - x * exp(3*x)).
%F A368177 a(n) = Sum_{k=1..n} (3*k)^(n-k) * (k-1)! * binomial(n,k).
%F A368177 a(n) ~ (n-1)! * 3^n / LambertW(3)^n. - _Vaclav Kotesovec_, Mar 11 2024
%t A368177 With[{nn=20},CoefficientList[Series[-Log[1-x Exp[3x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 10 2024 *)
%o A368177 (PARI) a(n) = sum(k=1, n, (3*k)^(n-k)*(k-1)!*binomial(n, k));
%Y A368177 Cf. A009306, A009444, A368176.
%Y A368177 Cf. A336951.
%K A368177 nonn,easy
%O A368177 0,3
%A A368177 _Seiichi Manyama_, Dec 14 2023