%I #11 Dec 04 2023 06:35:33
%S 1,0,4,12,128,1040,12672,161728,2481152,41806080,791613440,
%T 16399944704,371591995392,9110211874816,240670782291968,
%U 6810264853463040,205583847590985728,6593508525460226048,223913466256013918208,8026367531323488993280
%N Expansion of e.g.f. 1/(1 - x * (exp(2*x) - 1)).
%F a(0) = 1; a(n) = n * Sum_{k=2..n} 2^(k-1) * binomial(n-1,k-1) * a(n-k).
%F a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-k) * k! * Stirling2(n-k,k)/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, 2^(n-k)*k!*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A052848, A367886.
%Y Cf. A337038, A351736.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Dec 04 2023