%I #14 Jan 13 2024 06:55:33
%S 1,0,2,3,16,75,456,3185,25488,229383,2293840,25232229,302786760,
%T 3936227867,55107190152,826607852265,13225725636256,224837335816335,
%U 4047072044694048,76894368849186893,1537887376983737880,32295634916658495459,710503968166486900120,16341591267829198702737
%N a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * k / k!).
%F a(0) = 1; a(n) = n*a(n-1) + (-1)^n * n.
%F a(n) = n! - A000240(n).
%F E.g.f.: (1 - x * exp(-x)) / (1-x).
%F a(n) ~ (1 - exp(-1)) * n!. - _Vaclav Kotesovec_, Jan 13 2024
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*exp(-x))/(1-x)))
%Y Cf. A368766, A368767, A368768.
%Y Cf. A000240, A033540.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jan 04 2024
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