%I #12 Sep 01 2024 10:49:33
%S 1,2,6,30,192,1520,14220,153720,1881600,25728192,388402560,6415960320,
%T 115078138560,2227056923520,46247253212160,1025696098627200,
%U 24195406204569600,604862279807385600,15973029429800002560,444299711254300661760,12983645995613669376000
%N Expansion of e.g.f. 1/(1 + (log(1 - x^2))/x)^2.
%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375798.
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)! * |Stirling1(n-k,n-2*k)|/(n-k)!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^2)/x)^2))
%o (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*abs(stirling(n-k, n-2*k, 1))/(n-k)!);
%Y Cf. A375798, A375807.
%Y Cf. A375680.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Aug 29 2024