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

0,9

Links

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

Formula

a(n) ~ (4*exp(15/8) - 3*exp(7/4)) * 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))))(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);

Crossrefs

Column k=8 of A222029.

Sequence in context: A055362 A246195 A246615 * A246218 A178140 A180369

Adjacent sequences: A291111 A291112 A291113 * A291115 A291116 A291117

Keyword

nonn

Author

Alois P. Heinz, Aug 17 2017

Status

approved