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A208240
Number of functions f:{1,2,...,n}->{1,2,...,n} with at least one cycle of length >= 3.
2
0, 0, 0, 2, 38, 674, 12824, 269016, 6242116, 159629984, 4474156304, 136638234842, 4521281961800, 161263788956178, 6171136558989856, 252297980348513264, 10978226724737842928, 506678120536777708544, 24726830423666093964224, 1272394054736096884141554
OFFSET
0,4
COMMENTS
a(n) = n^n - A209319(n). - Vaclav Kotesovec, Oct 09 2013
LINKS
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.
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]
CROSSREFS
Cf. A101334.
Sequence in context: A098772 A207320 A262585 * A075796 A230903 A246000
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jan 11 2013
STATUS
approved