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A246217 Number of endofunctions on [n] where the largest cycle length equals 7.

%I A246217 #6 Aug 21 2014 04:33:18
%S A246217 720,46080,2099520,86400000,3478701600,141893959680,5963619055680,
%T A246217 260480095349760,11874161338182000,565994948205772800,
%U A246217 28225084763940704640,1472185000741804277760,80257688278285346487360,4568639693232433397760000,271256500003796168962953600
%N A246217 Number of endofunctions on [n] where the largest cycle length equals 7.
%H A246217 Alois P. Heinz, <a href="/A246217/b246217.txt">Table of n, a(n) for n = 7..200</a>
%F A246217 a(n) ~ (7*exp(363/140) - 6*exp(49/20)) * n^(n-1). - _Vaclav Kotesovec_, Aug 21 2014
%p A246217 with(combinat):
%p A246217 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246217       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A246217       b(n-i*j, i-1), j=0..n/i)))
%p A246217     end:
%p A246217 A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, min(j, k)), j=0..n):
%p A246217 a:= n-> A(n, 7) -A(n, 6):
%p A246217 seq(a(n), n=7..25);
%Y A246217 Column k=7 of A241981.
%K A246217 nonn
%O A246217 7,1
%A A246217 _Alois P. Heinz_, Aug 19 2014