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

Author

Alois P. Heinz, Aug 19 2014

Keywords

• nonn

Links

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

Crossrefs

Column k=6 of A241981.

Programs

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);

Formula

a(n) ~ (6*exp(49/20) - 5*exp(137/60)) * n^(n-1). - Vaclav Kotesovec, Aug 21 2014