A246196 Number of endofunctions on [n] where the smallest cycle length equals 9.

40320, 3628800, 219542400, 11496038400, 570031862400, 27908676956160, 1379187810000000, 69648048665395200, 3619848890071814400, 194427690066299289600, 10817193383227574703360, 624124327363867459584000, 37361601302439627939398400, 2320453709453248711940505600

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