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A246193 Number of endofunctions on [n] where the smallest cycle length equals 6.

%I A246193 #6 Aug 21 2014 05:30:03
%S A246193 120,5040,161280,4898880,151200000,4870182240,165549605760,
%T A246193 5964805154880,228051369786240,9247246914906000,397146441431900160,
%U A246193 18033691478872567680,864117601222345666560,43606402916521420059840,2312912761606956925440000,128696545326829348772023680
%N A246193 Number of endofunctions on [n] where the smallest cycle length equals 6.
%H A246193 Alois P. Heinz, <a href="/A246193/b246193.txt">Table of n, a(n) for n = 6..200</a>
%F A246193 a(n) ~ (exp(-137/60) - exp(-49/20)) * n^n. - _Vaclav Kotesovec_, Aug 21 2014
%p A246193 with(combinat):
%p A246193 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
%p A246193       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A246193       b(n-i*j, i+1), j=0..n/i)))
%p A246193     end:
%p A246193 A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
%p A246193 a:= n-> A(n, 6) -A(n, 7):
%p A246193 seq(a(n), n=6..25);
%Y A246193 Column k=6 of A246049.
%K A246193 nonn
%O A246193 6,1
%A A246193 _Alois P. Heinz_, Aug 18 2014