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%I #11 May 24 2022 08:11:30
%S 1,0,1,3,22,180,1902,23730,344872,5706288,105960600,2181449160,
%T 49311653616,1214109056160,32339248301808,926527371653520,
%U 28410493609687680,928335829570087680,32201658919855225728,1181755749910942408320,45744743939940787150080
%N Expansion of e.g.f. 1/(1 + x/4 * log(1 - 2 * x)).
%F a(0) = 1; a(n) = n! * Sum_{k=2..n} 2^(k-3)/(k-1) * a(n-k)/(n-k)!.
%F a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-3*k) * k! * |Stirling1(n-k,k)|/(n-k)!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x/4*log(1-2*x))))
%o (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-3)/(j-1)*v[i-j+1]/(i-j)!)); v;
%o (PARI) a(n) = n!*sum(k=0, n\2, 2^(n-3*k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);
%Y Cf. A052830, A187735, A354325, A354328.
%K nonn
%O 0,4
%A _Seiichi Manyama_, May 24 2022
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