%I #9 Dec 19 2023 09:16:44
%S 1,0,8,46,584,8138,139252,2770206,63009648,1612255186,45837395564,
%T 1433503025414,48906419204392,1807570412699322,71946432680652324,
%U 3068220235065662062,139570141248903198944,6745706553985526731682,345212056986241161670876
%N Expansion of e.g.f. exp(-2*x) / (1 - 2*x*exp(x)).
%F a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k-2)^k / k!.
%o (PARI) a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k-2)^k/k!);
%Y Cf. A351762, A368236, A368267, A368268.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Dec 19 2023