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A246194 Number of endofunctions on [n] where the smallest cycle length equals 7.

%I A246194 #6 Aug 21 2014 05:31:20
%S A246194 720,40320,1632960,60480000,2213719200,82771476480,3211179491520,
%T A246194 130241382036480,5541589755702000,247667354552217600,
%U A246194 11627089698327143040,573008938660751523840,29613698207957813302080,1602975684200327700480000,90757379602253683020931200
%N A246194 Number of endofunctions on [n] where the smallest cycle length equals 7.
%H A246194 Alois P. Heinz, <a href="/A246194/b246194.txt">Table of n, a(n) for n = 7..200</a>
%F A246194 a(n) ~ (exp(-49/20) - exp(-363/140)) * n^n. - _Vaclav Kotesovec_, Aug 21 2014
%p A246194 with(combinat):
%p A246194 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
%p A246194       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A246194       b(n-i*j, i+1), j=0..n/i)))
%p A246194     end:
%p A246194 A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
%p A246194 a:= n-> A(n, 7) -A(n, 8):
%p A246194 seq(a(n), n=7..25);
%Y A246194 Column k=7 of A246049.
%K A246194 nonn
%O A246194 7,1
%A A246194 _Alois P. Heinz_, Aug 18 2014