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A246216 Number of endofunctions on [n] where the largest cycle length equals 6.

%I A246216 #6 Aug 21 2014 04:31:13
%S A246216 120,5880,215040,7348320,252000000,8928667440,331079253120,
%T A246216 12919902035040,531665809234560,23074929870993000,1055390757120860160,
%U A246216 50802829404718896960,2569731417499060039680,136361684705644061566560,7578327282420081922560000
%N A246216 Number of endofunctions on [n] where the largest cycle length equals 6.
%H A246216 Alois P. Heinz, <a href="/A246216/b246216.txt">Table of n, a(n) for n = 6..200</a>
%F A246216 a(n) ~ (6*exp(49/20) - 5*exp(137/60)) * n^(n-1). - _Vaclav Kotesovec_, Aug 21 2014
%p A246216 with(combinat):
%p A246216 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246216       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A246216       b(n-i*j, i-1), j=0..n/i)))
%p A246216     end:
%p A246216 A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, min(j, k)), j=0..n):
%p A246216 a:= n-> A(n, 6) -A(n, 5):
%p A246216 seq(a(n), n=6..25);
%Y A246216 Column k=6 of A241981.
%K A246216 nonn
%O A246216 6,1
%A A246216 _Alois P. Heinz_, Aug 19 2014