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A240685 Number of forests with n labeled nodes and 8 trees.

%I A240685 #9 Sep 06 2014 15:15:21
%S A240685 1,36,990,26070,705375,20151846,614506893,20073049425,702495121185,
%T A240685 26300384653400,1050925859466912,44702294310795888,
%U A240685 2018603140944000000,96508616036970572820,4872478522317533107200,259140537891648535707618,14485018396686799073181696
%N A240685 Number of forests with n labeled nodes and 8 trees.
%H A240685 Alois P. Heinz, <a href="/A240685/b240685.txt">Table of n, a(n) for n = 8..200</a>
%F A240685 a(n) = n^(n-16) * (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^7 + 63*n^6 + 2135*n^5 + 49245*n^4 + 816256*n^3 + 9527868*n^2 + 71254800*n + 259459200)/645120. - _Vaclav Kotesovec_, Sep 06 2014
%p A240685 T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,
%p A240685       `if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*
%p A240685        T(n-j, m-1), j=1..n-m+1))))
%p A240685     end:
%p A240685 a:= n-> T(n, 8):
%p A240685 seq(a(n), n=8..30);
%t A240685 Table[n^(n-16) * (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^7 + 63*n^6 + 2135*n^5 + 49245*n^4 + 816256*n^3 + 9527868*n^2 + 71254800*n + 259459200)/645120,{n,8,25}] (* _Vaclav Kotesovec_, Sep 06 2014 *)
%Y A240685 Column m=8 of A105599. A diagonal of A138464.
%K A240685 nonn
%O A240685 8,2
%A A240685 _Alois P. Heinz_, Apr 10 2014