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%I #23 May 12 2022 15:18:52
%S 1,0,0,6,12,40,900,6048,43680,717120,8658720,102231360,1735525440,
%T 28819964160,473955850368,9235543363200,189202617676800,
%U 3940225003653120,89804740509434880,2169337606086389760,54085753764912844800,1429100881569205125120
%N Expansion of e.g.f. 1/(1 + x^2 * log(1 - x)).
%H Seiichi Manyama, <a href="/A351503/b351503.txt">Table of n, a(n) for n = 0..433</a>
%F a(0) = 1; a(n) = n! * Sum_{k=3..n} 1/(k-2) * a(n-k)/(n-k)!.
%F a(n) = n! * Sum_{k=0..floor(n/3)} k! * |Stirling1(n-2*k,k)|/(n-2*k)!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^2*log(1-x))))
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=3, i, 1/(j-2)*v[i-j+1]/(i-j)!)); v;
%o (PARI) a(n) = n!*sum(k=0, n\3, k!*abs(stirling(n-2*k, k, 1))/(n-2*k)!);
%Y Cf. A052830, A351504.
%Y Cf. A351505, A353228.
%K nonn
%O 0,4
%A _Seiichi Manyama_, May 04 2022
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