A246195 Number of endofunctions on [n] where the smallest cycle length equals 8.

5040, 362880, 18144000, 804988800, 34488115200, 1482082842240, 65120246231040, 2955402450000000, 139296260790086400, 6837541748945107200, 349978565353512775680, 18685433917574232157440, 1040347501174674201600000, 60368458528123335777196800

Offset: 8

Author

Alois P. Heinz, Aug 18 2014

Keywords

• nonn

Links

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

Crossrefs

Column k=8 of A246049.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 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, k), j=0..n):
a:= n-> A(n, 8) -A(n, 9):
seq(a(n), n=8..25);

Formula

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