A246193 - OEIS

%I #6 Aug 21 2014 05:30:03

%S 120,5040,161280,4898880,151200000,4870182240,165549605760,

%T 5964805154880,228051369786240,9247246914906000,397146441431900160,

%U 18033691478872567680,864117601222345666560,43606402916521420059840,2312912761606956925440000,128696545326829348772023680

%N Number of endofunctions on [n] where the smallest cycle length equals 6.

%H Alois P. Heinz, <a href="/A246193/b246193.txt">Table of n, a(n) for n = 6..200</a>

%F a(n) ~ (exp(-137/60) - exp(-49/20)) * 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, 6) -A(n, 7):

%p seq(a(n), n=6..25);

%Y Column k=6 of A246049.

%K nonn

%O 6,1

%A _Alois P. Heinz_, Aug 18 2014