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A240684 Number of forests with n labeled nodes and 7 trees.

%I A240684 #9 Sep 06 2014 15:09:49
%S A240684 1,28,630,14070,331485,8411634,231354123,6899167275,222569372025,
%T A240684 7741879425280,289297137120992,11570476164077376,493535471267193810,
%U A240684 22376155441920000000,1074961750207964923710,54561107576767408522752,2918071167402563863036269
%N A240684 Number of forests with n labeled nodes and 7 trees.
%H A240684 Alois P. Heinz, <a href="/A240684/b240684.txt">Table of n, a(n) for n = 7..200</a>
%F A240684 a(n) = n^(n-14) * (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^6 + 51*n^5 + 1385*n^4 + 24885*n^3 + 303766*n^2 + 2333976*n + 8648640)/46080. - _Vaclav Kotesovec_, Sep 06 2014
%p A240684 T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,
%p A240684       `if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*
%p A240684        T(n-j, m-1), j=1..n-m+1))))
%p A240684     end:
%p A240684 a:= n-> T(n, 7):
%p A240684 seq(a(n), n=7..30);
%t A240684 Table[n^(n-14) * (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^6 + 51*n^5 + 1385*n^4 + 24885*n^3 + 303766*n^2 + 2333976*n + 8648640)/46080,{n,7,25}] (* _Vaclav Kotesovec_, Sep 06 2014 *)
%Y A240684 Column m=7 of A105599. A diagonal of A138464.
%K A240684 nonn
%O A240684 7,2
%A A240684 _Alois P. Heinz_, Apr 10 2014