A246219 Number of endofunctions on [n] where the largest cycle length equals 9.

40320, 4032000, 268329600, 15328051200, 823379356800, 43413497487360, 2298646350000000, 123818753182924800, 6837492347913427200, 388855261570122547200, 22836250136299660220160, 1386932177757615390720000, 87175183432121364413433600, 5671938409008942797114572800

Offset: 9

Author

Alois P. Heinz, Aug 19 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..200

Crossrefs

Column k=9 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, 9) -A(n, 8):
seq(a(n), n=9..25);

Formula

a(n) ~ (9*exp(7129/2520) - 8*exp(761/280)) * n^(n-1). - Vaclav Kotesovec, Aug 21 2014