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A291110 Number of endofunctions on [n] such that the LCM of their cycle lengths equals four.

%I A291110 #13 Dec 29 2020 09:04:20
%S A291110 0,0,0,0,6,150,3240,71610,1692180,43296120,1202014800,36144686160,
%T A291110 1173334341960,40964232699390,1532291272031520,61185138170697450,
%U A291110 2599160146594218480,117091760635760465520,5577733223175044859840,280195572152151651031200
%N A291110 Number of endofunctions on [n] such that the LCM of their cycle lengths equals four.
%H A291110 Alois P. Heinz, <a href="/A291110/b291110.txt">Table of n, a(n) for n = 0..387</a>
%F A291110 a(n) ~ (3*exp(7/4) - 2*exp(3/2)) * n^(n-1). - _Vaclav Kotesovec_, Aug 18 2017
%p A291110 b:= proc(n, m) option remember; (k-> `if`(m>k, 0,
%p A291110       `if`(n=0, `if`(m=k, 1, 0), add(b(n-j, ilcm(m, j))
%p A291110        *binomial(n-1, j-1)*(j-1)!, j=1..n))))(4)
%p A291110     end:
%p A291110 a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A291110 seq(a(n), n=0..22);
%t A291110 b[n_, m_] := b[n, m] = With[{k = 4}, If[m > k, 0, If[n == 0, If[m == k, 1, 0], Sum[b[n - j, LCM[m, j]] Binomial[n-1, j - 1] (j-1)!, {j, 1, n}]]]];
%t A291110 a[n_] := If[n == 0, 0, Sum[b[j, 1] n^(n-j) Binomial[n-1, j-1], {j, 0, n}]];
%t A291110 a /@ Range[0, 22] (* _Jean-François Alcover_, Dec 29 2020, after _Alois P. Heinz_ *)
%Y A291110 Column k=4 of A222029.
%K A291110 nonn
%O A291110 0,5
%A A291110 _Alois P. Heinz_, Aug 17 2017