A246217 Number of endofunctions on [n] where the largest cycle length equals 7.

720, 46080, 2099520, 86400000, 3478701600, 141893959680, 5963619055680, 260480095349760, 11874161338182000, 565994948205772800, 28225084763940704640, 1472185000741804277760, 80257688278285346487360, 4568639693232433397760000, 271256500003796168962953600

Offset

7,1

Links

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

Formula

a(n) ~ (7*exp(363/140) - 6*exp(49/20)) * 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, 7) -A(n, 6):
seq(a(n), n=7..25);

Crossrefs

Column k=7 of A241981.

Sequence in context: A246194 A246614 A291113 * A364771 A003931 A158049

Adjacent sequences: A246214 A246215 A246216 * A246218 A246219 A246220

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2014

Status

approved