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

0, 0, 0, 2, 38, 674, 12824, 269016, 6242116, 159629984, 4474156304, 136638234842, 4521281961800, 161263788956178, 6171136558989856, 252297980348513264, 10978226724737842928, 506678120536777708544, 24726830423666093964224, 1272394054736096884141554

Offset: 0

Author

Geoffrey Critzer, Jan 11 2013

Keywords

• nonn

Comments

a(n) = n^n - A209319(n). - Vaclav Kotesovec, Oct 09 2013

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A101334.

Programs

Maple

T:= -LambertW(-x):
egf:= 1/(1-T) -exp(T +T^2/2):
a:= n-> n! *coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..20);  # Alois P. Heinz, Jan 11 2013

Mathematica

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]

Formula

E.g.f.: 1/(1-T(x)) - exp(T(x) + T(x)^2/2) where T(x) is the e.g.f. for A000169.