A116956 Number of functions f:{1,2,...,n}->{1,2,...,n} with odd cycles only.

1, 1, 3, 18, 157, 1800, 25551, 432376, 8494809, 190029888, 4768313275, 132626098176, 4049755214517, 134677876657792, 4845193429684167, 187490897290080000, 7765153170076158001, 342721890859339812864, 16058392049508837366771, 796093438190851834236928

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..386

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

Cf. A070896, A060281, A060435, A070896.

Cf. A212599.

Sequence in context: A246523 A246529 A305824 * A166887 A075678 A341331

Adjacent sequences: A116953 A116954 A116955 * A116957 A116958 A116959

Keyword

easy,nonn

Author

Vladeta Jovovic, Mar 30 2006

Status

approved