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 A354315 #11 May 24 2022 08:11:07
%S A354315 1,0,2,6,56,480,5664,75600,1182208,20829312,410768640,8943010560,
%T A354315 213187497984,5520777799680,154333888579584,4631752470159360,
%U A354315 148523272512307200,5067610703150284800,183308248516478828544,7006773595450681589760,282194468488468121518080
%N A354315 Expansion of e.g.f. 1/(1 + x/2 * log(1 - 2 * x)).
%F A354315 a(0) = 1; a(n) = n! * Sum_{k=2..n} 2^(k-2)/(k-1) * a(n-k)/(n-k)!.
%F A354315 a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-2*k) * k! * |Stirling1(n-k,k)|/(n-k)!.
%o A354315 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x/2*log(1-2*x))))
%o A354315 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=2, i, 2^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
%o A354315 (PARI) a(n) = n!*sum(k=0, n\2, 2^(n-2*k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);
%Y A354315 Cf. A052830, A354316.
%Y A354315 Cf. A354309, A354327.
%K A354315 nonn
%O A354315 0,3
%A A354315 _Seiichi Manyama_, May 23 2022