A246216 Number of endofunctions on [n] where the largest cycle length equals 6.

120, 5880, 215040, 7348320, 252000000, 8928667440, 331079253120, 12919902035040, 531665809234560, 23074929870993000, 1055390757120860160, 50802829404718896960, 2569731417499060039680, 136361684705644061566560, 7578327282420081922560000

Offset

6,1

Links

Alois P. Heinz, Table of n, a(n) for n = 6..200

Formula

a(n) ~ (6*exp(49/20) - 5*exp(137/60)) * 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, 6) -A(n, 5):
seq(a(n), n=6..25);

Crossrefs

Column k=6 of A241981.

Sequence in context: A229636 A282431 A008661 * A246284 A289292 A061541

Adjacent sequences: A246213 A246214 A246215 * A246217 A246218 A246219

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2014

Status

approved