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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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

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

Adjacent sequences:  A208237 A208238 A208239 * A208241 A208242 A208243

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jan 11 2013

STATUS

approved

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Last modified October 22 13:19 EDT 2019. Contains 328318 sequences. (Running on oeis4.)