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

7,1

Links

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

Formula

a(n) ~ (exp(-49/20) - exp(-363/140)) * 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, 7) -A(n, 8):
seq(a(n), n=7..25);

Crossrefs

Column k=7 of A246049.

Sequence in context: A342074 A055361 A092716 * A246614 A291113 A246217

Adjacent sequences: A246191 A246192 A246193 * A246195 A246196 A246197

Keyword

nonn

Author

Alois P. Heinz, Aug 18 2014

Status

approved