A291114 Number of endofunctions on [n] such that the LCM of their cycle lengths equals eight.

0, 0, 0, 0, 0, 0, 0, 0, 5040, 408240, 22680000, 1105196400, 51492672000, 2386304640720, 112267476921600, 5422473658602000, 270574193944454400, 13996921541118516000, 752006571801610245120, 41994571006059763946400, 2437848824911611890688000

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=8 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))))(8)
    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) ~ (4*exp(15/8) - 3*exp(7/4)) * n^(n-1). - Vaclav Kotesovec, Aug 18 2017