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A246195 Number of endofunctions on [n] where the smallest cycle length equals 8.

%I A246195 #6 Aug 21 2014 05:32:35
%S A246195 5040,362880,18144000,804988800,34488115200,1482082842240,
%T A246195 65120246231040,2955402450000000,139296260790086400,
%U A246195 6837541748945107200,349978565353512775680,18685433917574232157440,1040347501174674201600000,60368458528123335777196800
%N A246195 Number of endofunctions on [n] where the smallest cycle length equals 8.
%H A246195 Alois P. Heinz, <a href="/A246195/b246195.txt">Table of n, a(n) for n = 8..200</a>
%F A246195 a(n) ~ (exp(-363/140) - exp(-761/280)) * n^n. - _Vaclav Kotesovec_, Aug 21 2014
%p A246195 with(combinat):
%p A246195 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
%p A246195       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A246195       b(n-i*j, i+1), j=0..n/i)))
%p A246195     end:
%p A246195 A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
%p A246195 a:= n-> A(n, 8) -A(n, 9):
%p A246195 seq(a(n), n=8..25);
%Y A246195 Column k=8 of A246049.
%K A246195 nonn
%O A246195 8,1
%A A246195 _Alois P. Heinz_, Aug 18 2014