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

0,6

Links

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

Formula

a(n) ~ (exp(1) - 2*exp(4/3) - 2*exp(3/2) + 4*exp(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))))(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);

Crossrefs

Column k=6 of A222029.

Sequence in context: A292417 A117798 A006424 * A362168 A192370 A113102

Adjacent sequences: A291109 A291110 A291111 * A291113 A291114 A291115

Keyword

nonn

Author

Alois P. Heinz, Aug 17 2017

Status

approved