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%I #14 Dec 29 2023 06:02:00
%S 1,3,17,145,1649,23441,399865,7957881,180997857,4631289697,
%T 131670338921,4117813225769,140486274499345,5192341564319313,
%U 206669931188282073,8813624820931402201,400922608851086766017,19377398675442025382081,991639882680576890150089
%N Expansion of e.g.f. 1/(exp(-x) - 2*x).
%F a(0) = 1; a(n) = 2*n*a(n-1) + Sum_{k=1..n} (-1)^(k-1) * binomial(n,k) * a(n-k).
%F a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k+1)^k / k!.
%F a(n) ~ n! / (2 * LambertW(1/2)^(n+1) * (LambertW(1/2) + 1)). - _Vaclav Kotesovec_, Dec 29 2023
%o (PARI) a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k+1)^k/k!);
%Y Cf. A072597, A368237.
%Y Cf. A336947, A368233.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Dec 18 2023
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