A246218 Number of endofunctions on [n] where the largest cycle length equals 8.

5040, 408240, 22680000, 1106859600, 51732172800, 2408384618640, 113960430904320, 5541379593750000, 278592031202284800, 14529619059476320800, 787422201081850414080, 44373594768472437642720, 2600326096882824360960000, 158404803877320370312773600

Offset

8,1

Links

Alois P. Heinz, Table of n, a(n) for n = 8..200

Formula

a(n) ~ (8*exp(761/280) - 7*exp(363/140)) * n^(n-1). - Vaclav Kotesovec, Aug 21 2014

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, 8) -A(n, 7):
seq(a(n), n=8..25);

Crossrefs

Column k=8 of A241981.

Sequence in context: A246195 A246615 A291114 * A178140 A180369 A053876

Adjacent sequences: A246215 A246216 A246217 * A246219 A246220 A246221

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2014

Status

approved