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A291114 Number of endofunctions on [n] such that the LCM of their cycle lengths equals eight.

%I A291114 #8 Aug 18 2017 09:08:25
%S A291114 0,0,0,0,0,0,0,0,5040,408240,22680000,1105196400,51492672000,
%T A291114 2386304640720,112267476921600,5422473658602000,270574193944454400,
%U A291114 13996921541118516000,752006571801610245120,41994571006059763946400,2437848824911611890688000
%N A291114 Number of endofunctions on [n] such that the LCM of their cycle lengths equals eight.
%H A291114 Alois P. Heinz, <a href="/A291114/b291114.txt">Table of n, a(n) for n = 0..387</a>
%F A291114 a(n) ~ (4*exp(15/8) - 3*exp(7/4)) * n^(n-1). - _Vaclav Kotesovec_, Aug 18 2017
%p A291114 b:= proc(n, m) option remember; (k-> `if`(m>k, 0,
%p A291114       `if`(n=0, `if`(m=k, 1, 0), add(b(n-j, ilcm(m, j))
%p A291114        *binomial(n-1, j-1)*(j-1)!, j=1..n))))(8)
%p A291114     end:
%p A291114 a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A291114 seq(a(n), n=0..22);
%Y A291114 Column k=8 of A222029.
%K A291114 nonn
%O A291114 0,9
%A A291114 _Alois P. Heinz_, Aug 17 2017