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A291112 Number of endofunctions on [n] such that the LCM of their cycle lengths equals six.

%I A291112 #8 Aug 18 2017 10:51:29
%S A291112 0,0,0,0,0,20,840,26250,773920,23166360,724253040,23921630810,
%T A291112 838352908800,31203417745500,1232550480801640,51590674307982810,
%U A291112 2283883442833836480,106713738151299297200,5251783507905871571040,271673904611812139017650,14743195769771119241426080
%N A291112 Number of endofunctions on [n] such that the LCM of their cycle lengths equals six.
%H A291112 Alois P. Heinz, <a href="/A291112/b291112.txt">Table of n, a(n) for n = 0..386</a>
%F A291112 a(n) ~ (exp(1) - 2*exp(4/3) - 2*exp(3/2) + 4*exp(2)) * n^(n-1). - _Vaclav Kotesovec_, Aug 18 2017
%p A291112 b:= proc(n, m) option remember; (k-> `if`(m>k, 0,
%p A291112       `if`(n=0, `if`(m=k, 1, 0), add(b(n-j, ilcm(m, j))
%p A291112        *binomial(n-1, j-1)*(j-1)!, j=1..n))))(6)
%p A291112     end:
%p A291112 a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A291112 seq(a(n), n=0..22);
%Y A291112 Column k=6 of A222029.
%K A291112 nonn
%O A291112 0,6
%A A291112 _Alois P. Heinz_, Aug 17 2017