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A246219 Number of endofunctions on [n] where the largest cycle length equals 9. 2
40320, 4032000, 268329600, 15328051200, 823379356800, 43413497487360, 2298646350000000, 123818753182924800, 6837492347913427200, 388855261570122547200, 22836250136299660220160, 1386932177757615390720000, 87175183432121364413433600, 5671938409008942797114572800 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 17 02:55 EDT 2022. Contains 353727 sequences. (Running on oeis4.)