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A246220 Number of endofunctions on [n] where the largest cycle length equals 10. 2
362880, 43908480, 3448811520, 228012744960, 13954338478080, 827512686000000, 48753634065776640, 2895879112057451520, 174984885490926551040, 10817178515493080290560, 686533182382689959116800, 44833266187415969387604480, 3016487768851293040555130880 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,1

COMMENTS

In general, number of endofunctions on [n] where the largest cycle length equals k is asymptotic to (k*exp(H(k)) - (k-1)*exp(H(k-1))) * n^(n-1), where H(k) is the harmonic number A001008/A002805, k>=1. - Vaclav Kotesovec, Aug 21 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 10..200

FORMULA

a(n) ~ (10*exp(7381/2520) - 9*exp(7129/2520)) * 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, 10) -A(n, 9):

seq(a(n), n=10..25);

CROSSREFS

Column k=10 of A241981.

Sequence in context: A179064 A246197 A246617 * A160319 A227671 A172536

Adjacent sequences:  A246217 A246218 A246219 * A246221 A246222 A246223

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 19 2014

STATUS

approved

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Last modified December 3 02:31 EST 2021. Contains 349445 sequences. (Running on oeis4.)