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A116956
Number of functions f:{1,2,...,n}->{1,2,...,n} with odd cycles only.
9
1, 1, 3, 18, 157, 1800, 25551, 432376, 8494809, 190029888, 4768313275, 132626098176, 4049755214517, 134677876657792, 4845193429684167, 187490897290080000, 7765153170076158001, 342721890859339812864, 16058392049508837366771, 796093438190851834236928
OFFSET
0,3
LINKS
FORMULA
E.g.f.: sqrt((1-LambertW(-x))/(1+LambertW(-x))).
Sum_{k=0..n} binomial(n,k)*a(k)*a(n-k) = 2*n^n, n>0. - Vladeta Jovovic, Oct 11 2007
a(n) ~ n! * 2^(3/4)*Gamma(3/4)*exp(n)/(2*Pi*n^(3/4)). - Vaclav Kotesovec, Sep 24 2013
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)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, May 20 2016
MATHEMATICA
t = Sum[n^(n - 1) x^n/n!, {n, 1, 20}]; Range[0, 20]! CoefficientList[
Series[((1 + t)/(1 - t))^(1/2), {x, 0, 20}], x] (* Geoffrey Critzer, Dec 07 2011 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Mar 30 2006
STATUS
approved