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%I #15 Aug 25 2024 09:58:12
%S 1,0,0,3,6,20,360,2394,17220,252720,2963520,34525260,552027960,
%T 8860952880,142907532768,2682870913800,53297669552400,
%U 1086135012144000,24087251436249600,566843973576536880,13834256829134364000,357412359616922433600,9723652519748883408000
%N Expansion of e.g.f. 1 / sqrt(1 + x^2 * log(1 - x)).
%F a(n) = n! * Sum_{k=0..floor(n/3)} A001147(k) * |Stirling1(n-2*k,k)|/(2^k*(n-2*k)!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1+x^2*log(1-x))))
%o (PARI) a001147(n) = prod(k=0, n-1, 2*k+1);
%o a(n) = n!*sum(k=0, n\3, a001147(k)*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
%Y Cf. A001147, A351503, A351505, A375715.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Aug 25 2024