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A208240 Number of functions f:{1,2,...,n}->{1,2,...,n} with at least one cycle of length >= 3.

%I A208240 #14 Oct 09 2013 03:13:15
%S A208240 0,0,0,2,38,674,12824,269016,6242116,159629984,4474156304,
%T A208240 136638234842,4521281961800,161263788956178,6171136558989856,
%U A208240 252297980348513264,10978226724737842928,506678120536777708544,24726830423666093964224,1272394054736096884141554
%N A208240 Number of functions f:{1,2,...,n}->{1,2,...,n} with at least one cycle of length >= 3.
%C A208240 a(n) = n^n - A209319(n). - _Vaclav Kotesovec_, Oct 09 2013
%H A208240 Alois P. Heinz, <a href="/A208240/b208240.txt">Table of n, a(n) for n = 0..150</a>
%F A208240 E.g.f.: 1/(1-T(x)) - exp(T(x) + T(x)^2/2) where T(x) is the e.g.f. for A000169.
%p A208240 T:= -LambertW(-x):
%p A208240 egf:= 1/(1-T) -exp(T +T^2/2):
%p A208240 a:= n-> n! *coeff(series(egf, x, n+1), x, n):
%p A208240 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jan 11 2013
%t A208240 nn=20;t=Sum[n^(n-1)x^n/n!,{n,1,nn}];Range[0,nn]!CoefficientList[Series[1/(1-t)-Exp[Sum[t^i/i,{i,1,2}]],{x,0,nn}],x]
%Y A208240 Cf. A101334.
%K A208240 nonn
%O A208240 0,4
%A A208240 _Geoffrey Critzer_, Jan 11 2013