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A240687 Number of forests with n labeled nodes and 10 trees.

%I A240687 #9 Sep 06 2014 15:23:18
%S A240687 1,55,2145,75790,2637635,93783690,3467403940,134463763720,
%T A240687 5491244257785,236503301350745,10742799174110575,514243815022230930,
%U A240687 25908948794088640280,1371861202568610407885,76216658109172817448960,4435598473883166992187500,269963484584876515488140800
%N A240687 Number of forests with n labeled nodes and 10 trees.
%H A240687 Alois P. Heinz, <a href="/A240687/b240687.txt">Table of n, a(n) for n = 10..200</a>
%F A240687 a(n) = n^(n-20) * (n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^9 + 90*n^8 + 4386*n^7 + 149436*n^6 + 3859401*n^5 + 77149170*n^4 + 1176873076*n^3 + 13044397176*n^2 + 94273812000*n + 335221286400)/185794560. - _Vaclav Kotesovec_, Sep 06 2014
%p A240687 T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,
%p A240687       `if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*
%p A240687        T(n-j, m-1), j=1..n-m+1))))
%p A240687     end:
%p A240687 a:= n-> T(n, 10):
%p A240687 seq(a(n), n=10..30);
%t A240687 Table[n^(n-20) * (n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^9 + 90*n^8 + 4386*n^7 + 149436*n^6 + 3859401*n^5 + 77149170*n^4 + 1176873076*n^3 + 13044397176*n^2 + 94273812000*n + 335221286400)/185794560,{n,10,30}] (* _Vaclav Kotesovec_, Sep 06 2014 *)
%Y A240687 Column m=10 of A105599. A diagonal of A138464.
%K A240687 nonn
%O A240687 10,2
%A A240687 _Alois P. Heinz_, Apr 10 2014