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

9,1

Links

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

Formula

a(n) ~ (9*exp(7129/2520) - 8*exp(761/280)) * 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, 9) -A(n, 8):
seq(a(n), n=9..25);

Crossrefs

Column k=9 of A241981.

Sequence in context: A246196 A246616 A291115 * A045516 A160318 A227670

Adjacent sequences: A246216 A246217 A246218 * A246220 A246221 A246222

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2014

Status

approved