OFFSET
0,3
COMMENTS
Equivalently, these are the functions counted by A116956 with the additional constraint that every element is mapped to a recurrent element. A recurrent element is an element on a cycle in the functional digraph.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..411
FORMULA
E.g.f.: sqrt((1 + z*exp(z))/(1 - z*exp(z))).
Exponential transform of A216401.
a(n) ~ 2 * n^n / (sqrt(1+LambertW(1)) * LambertW(1)^n * exp(n)). - Vaclav Kotesovec, Jun 26 2022
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(`if`(j::odd,
(j-1)!*b(n-j)*binomial(n-1, j-1), 0), j=1..n))
end:
a:= n-> add(b(j)*j^(n-j)*binomial(n, j), j=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, Jul 25 2016
MATHEMATICA
nn = 20; Range[0, nn]! CoefficientList[Series[Sqrt[(1 + z*Exp[z])/(1 - z*Exp[z])], {z, 0, nn}], z]
PROG
(PARI) default(seriesprecision, 30);
S=sqrt((1 + x*exp(x))/(1 - x*exp(x)));
v=Vec(S); for(n=2, #v-1, v[n+1]*=n!); v \\ Charles R Greathouse IV, Jul 29 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jul 25 2016
STATUS
approved