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

%I A208230 #11 May 20 2016 05:55:46
%S A208230 1,0,0,0,6,144,3000,64560,1498140,37906848,1046608416,31438821600,
%T A208230 1023129229320,35910464987760,1353422643322464,54548490915316944,
%U A208230 2342204085734058000,106771822456475695680,5151207243866077428480,262261296920723111462592,14053817061169685865626976
%N A208230 Number of functions f:{1,2,...,n}->{1,2,...,n} with all cycles of length >= 4.
%H A208230 Alois P. Heinz, <a href="/A208230/b208230.txt">Table of n, a(n) for n = 0..386</a>
%F A208230 E.g.f.: exp( Sum_{i>=4} T(x)^i/i )  where T(x) is the e.g.f. for A000169
%p A208230 b:= proc(n) option remember; `if`(n=0, 1, add(
%p A208230       b(n-j)*binomial(n-1, j-1)*(j-1)!, j=4..n))
%p A208230     end:
%p A208230 a:= n-> add(b(j)*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A208230 seq(a(n), n=0..25);  # _Alois P. Heinz_, May 20 2016
%t A208230 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]
%Y A208230 Cf. A000312, A065440, A134362.
%K A208230 nonn
%O A208230 0,5
%A A208230 _Geoffrey Critzer_, Jan 10 2013