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A240681 Number of forests with n labeled nodes and 4 trees.

%I A240681 #10 Sep 06 2014 14:51:26
%S A240681 1,10,105,1295,18865,320544,6258000,138437310,3428282880,94059655690,
%T A240681 2833936641536,93055995703125,3308477732618240,126642365068676240,
%U A240681 5193315990469140480,227160198500847385884,10557603840000000000000,519578655591970045435770
%N A240681 Number of forests with n labeled nodes and 4 trees.
%H A240681 Alois P. Heinz, <a href="/A240681/b240681.txt">Table of n, a(n) for n = 4..200</a>
%F A240681 a(n) = n^(n-8) * (n-3)*(n-2)*(n-1)*(n^3 + 21*n^2 + 202*n + 840)/48. - _Vaclav Kotesovec_, Sep 06 2014
%p A240681 T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,
%p A240681       `if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*
%p A240681        T(n-j, m-1), j=1..n-m+1))))
%p A240681     end:
%p A240681 a:= n-> T(n, 4):
%p A240681 seq(a(n), n=4..30);
%t A240681 Table[n^(n-8) * (n-3)*(n-2)*(n-1)*(n^3 + 21*n^2 + 202*n + 840)/48,{n,4,20}] (* _Vaclav Kotesovec_, Sep 06 2014 *)
%Y A240681 Column m=4 of A105599. A diagonal of A138464.
%K A240681 nonn
%O A240681 4,2
%A A240681 _Alois P. Heinz_, Apr 10 2014