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A246218 Number of endofunctions on [n] where the largest cycle length equals 8.

%I A246218 #6 Aug 21 2014 04:35:32
%S A246218 5040,408240,22680000,1106859600,51732172800,2408384618640,
%T A246218 113960430904320,5541379593750000,278592031202284800,
%U A246218 14529619059476320800,787422201081850414080,44373594768472437642720,2600326096882824360960000,158404803877320370312773600
%N A246218 Number of endofunctions on [n] where the largest cycle length equals 8.
%H A246218 Alois P. Heinz, <a href="/A246218/b246218.txt">Table of n, a(n) for n = 8..200</a>
%F A246218 a(n) ~ (8*exp(761/280) - 7*exp(363/140)) * n^(n-1). - _Vaclav Kotesovec_, Aug 21 2014
%p A246218 with(combinat):
%p A246218 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246218       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A246218       b(n-i*j, i-1), j=0..n/i)))
%p A246218     end:
%p A246218 A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, min(j, k)), j=0..n):
%p A246218 a:= n-> A(n, 8) -A(n, 7):
%p A246218 seq(a(n), n=8..25);
%Y A246218 Column k=8 of A241981.
%K A246218 nonn
%O A246218 8,1
%A A246218 _Alois P. Heinz_, Aug 19 2014