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

Author

Alois P. Heinz, Aug 18 2014

Keywords

• nonn

Links

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

Crossrefs

Column k=9 of A246049.

Programs

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);

Formula

a(n) ~ (exp(-761/280) - exp(-7129/2520)) * n^n. - Vaclav Kotesovec, Aug 21 2014