A246217 Number of endofunctions on [n] where the largest cycle length equals 7.

720, 46080, 2099520, 86400000, 3478701600, 141893959680, 5963619055680, 260480095349760, 11874161338182000, 565994948205772800, 28225084763940704640, 1472185000741804277760, 80257688278285346487360, 4568639693232433397760000, 271256500003796168962953600

Offset: 7

Author

Alois P. Heinz, Aug 19 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..200

Crossrefs

Column k=7 of A241981.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
      b(n-i*j, i-1), j=0..n/i)))
    end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, min(j, k)), j=0..n):
a:= n-> A(n, 7) -A(n, 6):
seq(a(n), n=7..25);

Formula

a(n) ~ (7*exp(363/140) - 6*exp(49/20)) * n^(n-1). - Vaclav Kotesovec, Aug 21 2014