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

0, 0, 0, 0, 6, 150, 3240, 71610, 1692180, 43296120, 1202014800, 36144686160, 1173334341960, 40964232699390, 1532291272031520, 61185138170697450, 2599160146594218480, 117091760635760465520, 5577733223175044859840, 280195572152151651031200

Offset: 0

Author

Alois P. Heinz, Aug 17 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..387

Crossrefs

Column k=4 of A222029.

Programs

Maple

b:= proc(n, m) option remember; (k-> `if`(m>k, 0,
      `if`(n=0, `if`(m=k, 1, 0), add(b(n-j, ilcm(m, j))
       *binomial(n-1, j-1)*(j-1)!, j=1..n))))(4)
    end:
a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..22);

Mathematica

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}]]]];
a[n_] := If[n == 0, 0, Sum[b[j, 1] n^(n-j) Binomial[n-1, j-1], {j, 0, n}]];
a /@ Range[0, 22] (* Jean-François Alcover, Dec 29 2020, after Alois P. Heinz *)

Formula

a(n) ~ (3*exp(7/4) - 2*exp(3/2)) * n^(n-1). - Vaclav Kotesovec, Aug 18 2017