OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..350
FORMULA
E.g.f.: exp(T(x) + T(x)^2/2) = A(T(x)) where A(x) is the e.g.f. for A000085 and T(x) is the e.g.f. for A000169.
a(n) ~ 2*exp(3/2)*n^(n-1). - Vaclav Kotesovec, Sep 30 2013
EXAMPLE
a(3) = 25 because there are 27 functions from {1,2,3} into itself but 2 of these have cycle length of 3: 2,3,1, and 3,1,2.
MAPLE
T:= -LambertW(-x):
egf:= 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 19 2013
MATHEMATICA
nn=20; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0, nn]!CoefficientList[Series[Exp[Sum[t^i/i, {i, 1, 2}]], {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jan 19 2013
STATUS
approved