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A246196 Number of endofunctions on [n] where the smallest cycle length equals 9. 2
40320, 3628800, 219542400, 11496038400, 570031862400, 27908676956160, 1379187810000000, 69648048665395200, 3619848890071814400, 194427690066299289600, 10817193383227574703360, 624124327363867459584000, 37361601302439627939398400, 2320453709453248711940505600 (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) ~ (exp(-761/280) - exp(-7129/2520)) * n^n. - Vaclav Kotesovec, Aug 21 2014

MAPLE

with(combinat):

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 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, k), j=0..n):

a:= n-> A(n, 9) -A(n, 10):

seq(a(n), n=9..25);

CROSSREFS

Column k=9 of A246049.

Sequence in context: A228911 A213878 A179063 * A246616 A291115 A246219

Adjacent sequences:  A246193 A246194 A246195 * A246197 A246198 A246199

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 18 2014

STATUS

approved

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Last modified May 25 02:01 EDT 2020. Contains 334581 sequences. (Running on oeis4.)