A291113 Number of endofunctions on [n] such that the LCM of their cycle lengths equals seven.

0, 0, 0, 0, 0, 0, 0, 720, 46080, 2073600, 83635200, 3284582400, 130292997120, 5315938467840, 225174409574400, 9949921392153600, 459690572096870400, 22223242784959856640, 1124142765926532618240, 59464928954695680000000, 3286601083552719895603200

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=7 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))))(7)
    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) ~ (2*exp(8/7)-exp(1)) * n^(n-1). - Vaclav Kotesovec, Aug 18 2017