A208230 Number of functions f:{1,2,...,n}->{1,2,...,n} with all cycles of length >= 4.

1, 0, 0, 0, 6, 144, 3000, 64560, 1498140, 37906848, 1046608416, 31438821600, 1023129229320, 35910464987760, 1353422643322464, 54548490915316944, 2342204085734058000, 106771822456475695680, 5151207243866077428480, 262261296920723111462592, 14053817061169685865626976

Offset: 0

Author

Geoffrey Critzer, Jan 10 2013

Keywords

• nonn

Links

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

Crossrefs

Cf. A000312, A065440, A134362.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(
      b(n-j)*binomial(n-1, j-1)*(j-1)!, j=4..n))
    end:
a:= n-> add(b(j)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);  # Alois P. Heinz, May 20 2016

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,4,nn}]],{x,0,nn}],x]

Formula

E.g.f.: exp( Sum_{i>=4} T(x)^i/i ) where T(x) is the e.g.f. for A000169