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A240683 Number of forests with n labeled nodes and 6 trees.

%I A240683 #9 Sep 06 2014 15:05:35
%S A240683 1,21,378,7056,143325,3207897,79170399,2146836978,63641666088,
%T A240683 2051450651250,71530799628288,2684845732979592,107992630908804096,
%U A240683 4636019437800293718,211623646464000000000,10237455825414473977524,523244238837133507448832,28177157277452320985386539
%N A240683 Number of forests with n labeled nodes and 6 trees.
%H A240683 Alois P. Heinz, <a href="/A240683/b240683.txt">Table of n, a(n) for n = 6..200</a>
%F A240683 a(n) = n^(n-12) * (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^5 + 40*n^4 + 835*n^3 + 10960*n^2 + 87636*n + 332640)/3840. - _Vaclav Kotesovec_, Sep 06 2014
%p A240683 T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,
%p A240683       `if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*
%p A240683        T(n-j, m-1), j=1..n-m+1))))
%p A240683     end:
%p A240683 a:= n-> T(n, 6):
%p A240683 seq(a(n), n=6..30);
%t A240683 Table[n^(n-12) * (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^5 + 40*n^4 + 835*n^3 + 10960*n^2 + 87636*n + 332640)/3840,{n,6,25}] (* _Vaclav Kotesovec_, Sep 06 2014 *)
%Y A240683 Column m=6 of A105599. A diagonal of A138464.
%K A240683 nonn
%O A240683 6,2
%A A240683 _Alois P. Heinz_, Apr 10 2014