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

0,5

Links

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

Formula

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

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 *)

Crossrefs

Column k=4 of A222029.

Sequence in context: A056418 A346694 A070025 * A246214 A065946 A222051

Adjacent sequences: A291107 A291108 A291109 * A291111 A291112 A291113

Keyword

nonn

Author

Alois P. Heinz, Aug 17 2017

Status

approved