A291112 Number of endofunctions on [n] such that the LCM of their cycle lengths equals six.

0, 0, 0, 0, 0, 20, 840, 26250, 773920, 23166360, 724253040, 23921630810, 838352908800, 31203417745500, 1232550480801640, 51590674307982810, 2283883442833836480, 106713738151299297200, 5251783507905871571040, 271673904611812139017650, 14743195769771119241426080

Offset: 0

Author

Alois P. Heinz, Aug 17 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..386

Crossrefs

Column k=6 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))))(6)
    end:
a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..22);

Formula

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