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A246219 Number of endofunctions on [n] where the largest cycle length equals 9.

%I A246219 #6 Aug 21 2014 04:37:56
%S A246219 40320,4032000,268329600,15328051200,823379356800,43413497487360,
%T A246219 2298646350000000,123818753182924800,6837492347913427200,
%U A246219 388855261570122547200,22836250136299660220160,1386932177757615390720000,87175183432121364413433600,5671938409008942797114572800
%N A246219 Number of endofunctions on [n] where the largest cycle length equals 9.
%H A246219 Alois P. Heinz, <a href="/A246219/b246219.txt">Table of n, a(n) for n = 9..200</a>
%F A246219 a(n) ~ (9*exp(7129/2520) - 8*exp(761/280)) * n^(n-1). - _Vaclav Kotesovec_, Aug 21 2014
%p A246219 with(combinat):
%p A246219 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246219       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A246219       b(n-i*j, i-1), j=0..n/i)))
%p A246219     end:
%p A246219 A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, min(j, k)), j=0..n):
%p A246219 a:= n-> A(n, 9) -A(n, 8):
%p A246219 seq(a(n), n=9..25);
%Y A246219 Column k=9 of A241981.
%K A246219 nonn
%O A246219 9,1
%A A246219 _Alois P. Heinz_, Aug 19 2014