A246194 - OEIS

%I #6 Aug 21 2014 05:31:20

%S 720,40320,1632960,60480000,2213719200,82771476480,3211179491520,

%T 130241382036480,5541589755702000,247667354552217600,

%U 11627089698327143040,573008938660751523840,29613698207957813302080,1602975684200327700480000,90757379602253683020931200

%N Number of endofunctions on [n] where the smallest cycle length equals 7.

%H Alois P. Heinz, <a href="/A246194/b246194.txt">Table of n, a(n) for n = 7..200</a>

%F a(n) ~ (exp(-49/20) - exp(-363/140)) * 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, 7) -A(n, 8):

%p seq(a(n), n=7..25);

%Y Column k=7 of A246049.

%K nonn

%O 7,1

%A _Alois P. Heinz_, Aug 18 2014