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A246196 Number of endofunctions on [n] where the smallest cycle length equals 9.

%I A246196 #6 Aug 21 2014 05:33:52
%S A246196 40320,3628800,219542400,11496038400,570031862400,27908676956160,
%T A246196 1379187810000000,69648048665395200,3619848890071814400,
%U A246196 194427690066299289600,10817193383227574703360,624124327363867459584000,37361601302439627939398400,2320453709453248711940505600
%N A246196 Number of endofunctions on [n] where the smallest cycle length equals 9.
%H A246196 Alois P. Heinz, <a href="/A246196/b246196.txt">Table of n, a(n) for n = 9..200</a>
%F A246196 a(n) ~ (exp(-761/280) - exp(-7129/2520)) * n^n. - _Vaclav Kotesovec_, Aug 21 2014
%p A246196 with(combinat):
%p A246196 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
%p A246196       add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
%p A246196       b(n-i*j, i+1), j=0..n/i)))
%p A246196     end:
%p A246196 A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
%p A246196 a:= n-> A(n, 9) -A(n, 10):
%p A246196 seq(a(n), n=9..25);
%Y A246196 Column k=9 of A246049.
%K A246196 nonn
%O A246196 9,1
%A A246196 _Alois P. Heinz_, Aug 18 2014