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 A368445 #14 Jul 07 2025 12:03:50
%S A368445 1,4,34,469,8815,208348,5922118,196568419,7459854973,318560689324,
%T A368445 15116763184978,789119869380577,44939583072146251,2772582488089509028,
%U A368445 184216538154508055062,13114092114632287359919,995813104288130697683065,80342826520464644566291828
%N A368445 Expansion of e.g.f. exp(x) / (1 + log(1 - 3*x)).
%H A368445 Harvey P. Dale, <a href="/A368445/b368445.txt">Table of n, a(n) for n = 0..357</a>
%F A368445 a(n) = 1 + Sum_{k=1..n} 3^k * (k-1)! * binomial(n,k) * a(n-k).
%t A368445 With[{nn=20},CoefficientList[Series[Exp[x]/(1+Log[1-3x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 07 2025 *)
%o A368445 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=1, i, 3^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;
%Y A368445 Cf. A291979, A368444.
%Y A368445 Cf. A343709.
%K A368445 nonn
%O A368445 0,2
%A A368445 _Seiichi Manyama_, Dec 24 2023