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%I #9 Dec 19 2023 09:16:32
%S 1,1,9,71,817,11599,197881,3938087,89569761,2291869727,65159228521,
%T 2037767466679,69521938950289,2569515452879855,102274007835523161,
%U 4361566914028222919,198403133940750790081,9589223805173365594687,490729273233730201604809
%N Expansion of e.g.f. exp(-x) / (1 - 2*x*exp(x)).
%F a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k-1)^k / k!.
%o (PARI) a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k-1)^k/k!);
%Y Cf. A351762, A368236, A368267, A368269.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Dec 19 2023