A246194 Number of endofunctions on [n] where the smallest cycle length equals 7.

720, 40320, 1632960, 60480000, 2213719200, 82771476480, 3211179491520, 130241382036480, 5541589755702000, 247667354552217600, 11627089698327143040, 573008938660751523840, 29613698207957813302080, 1602975684200327700480000, 90757379602253683020931200

Offset: 7

Author

Alois P. Heinz, Aug 18 2014

Keywords

• nonn

Links

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

Crossrefs

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

Formula

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