A291110 - OEIS

%I #13 Dec 29 2020 09:04:20

%S 0,0,0,0,6,150,3240,71610,1692180,43296120,1202014800,36144686160,

%T 1173334341960,40964232699390,1532291272031520,61185138170697450,

%U 2599160146594218480,117091760635760465520,5577733223175044859840,280195572152151651031200

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

%H Alois P. Heinz, <a href="/A291110/b291110.txt">Table of n, a(n) for n = 0..387</a>

%F a(n) ~ (3*exp(7/4) - 2*exp(3/2)) * n^(n-1). - _Vaclav Kotesovec_, Aug 18 2017

%p b:= proc(n, m) option remember; (k-> `if`(m>k, 0,

%p       `if`(n=0, `if`(m=k, 1, 0), add(b(n-j, ilcm(m, j))

%p        *binomial(n-1, j-1)*(j-1)!, j=1..n))))(4)

%p     end:

%p a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):

%p seq(a(n), n=0..22);

%t 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 a[n_] := If[n == 0, 0, Sum[b[j, 1] n^(n-j) Binomial[n-1, j-1], {j, 0, n}]];

%t a /@ Range[0, 22] (* _Jean-François Alcover_, Dec 29 2020, after _Alois P. Heinz_ *)

%Y Column k=4 of A222029.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Aug 17 2017