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A291113 Number of endofunctions on [n] such that the LCM of their cycle lengths equals seven.

%I A291113 #6 Aug 18 2017 07:17:21
%S A291113 0,0,0,0,0,0,0,720,46080,2073600,83635200,3284582400,130292997120,
%T A291113 5315938467840,225174409574400,9949921392153600,459690572096870400,
%U A291113 22223242784959856640,1124142765926532618240,59464928954695680000000,3286601083552719895603200
%N A291113 Number of endofunctions on [n] such that the LCM of their cycle lengths equals seven.
%H A291113 Alois P. Heinz, <a href="/A291113/b291113.txt">Table of n, a(n) for n = 0..387</a>
%F A291113 a(n) ~ (2*exp(8/7)-exp(1)) * n^(n-1). - _Vaclav Kotesovec_, Aug 18 2017
%p A291113 b:= proc(n, m) option remember; (k-> `if`(m>k, 0,
%p A291113       `if`(n=0, `if`(m=k, 1, 0), add(b(n-j, ilcm(m, j))
%p A291113        *binomial(n-1, j-1)*(j-1)!, j=1..n))))(7)
%p A291113     end:
%p A291113 a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A291113 seq(a(n), n=0..22);
%Y A291113 Column k=7 of A222029.
%K A291113 nonn
%O A291113 0,8
%A A291113 _Alois P. Heinz_, Aug 17 2017