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

8,1

Links

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

Formula

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

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);

Crossrefs

Column k=8 of A246049.

Sequence in context: A179062 A342075 A055362 * A246615 A291114 A246218

Adjacent sequences: A246192 A246193 A246194 * A246196 A246197 A246198

Keyword

nonn

Author

Alois P. Heinz, Aug 18 2014

Status

approved