A246196 - OEIS

%I #6 Aug 21 2014 05:33:52

%S 40320,3628800,219542400,11496038400,570031862400,27908676956160,

%T 1379187810000000,69648048665395200,3619848890071814400,

%U 194427690066299289600,10817193383227574703360,624124327363867459584000,37361601302439627939398400,2320453709453248711940505600

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

%H Alois P. Heinz, <a href="/A246196/b246196.txt">Table of n, a(n) for n = 9..200</a>

%F a(n) ~ (exp(-761/280) - exp(-7129/2520)) * n^n. - _Vaclav Kotesovec_, Aug 21 2014

%p with(combinat):

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,

%p       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*

%p       b(n-i*j, i+1), j=0..n/i)))

%p     end:

%p A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):

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

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

%Y Column k=9 of A246049.

%K nonn

%O 9,1

%A _Alois P. Heinz_, Aug 18 2014