A208240 - OEIS

%I #14 Oct 09 2013 03:13:15

%S 0,0,0,2,38,674,12824,269016,6242116,159629984,4474156304,

%T 136638234842,4521281961800,161263788956178,6171136558989856,

%U 252297980348513264,10978226724737842928,506678120536777708544,24726830423666093964224,1272394054736096884141554

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

%C a(n) = n^n - A209319(n). - _Vaclav Kotesovec_, Oct 09 2013

%H Alois P. Heinz, <a href="/A208240/b208240.txt">Table of n, a(n) for n = 0..150</a>

%F 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 T:= -LambertW(-x):

%p egf:= 1/(1-T) -exp(T +T^2/2):

%p a:= n-> n! *coeff(series(egf, x, n+1), x, n):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Jan 11 2013

%t 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 Cf. A101334.

%K nonn

%O 0,4

%A _Geoffrey Critzer_, Jan 11 2013