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A215859 Number of simple labeled graphs on n nodes with exactly 9 connected components that are trees or cycles.

%I A215859 #8 Dec 04 2014 06:59:16
%S A215859 1,45,1650,54945,1795794,59546487,2043490735,73415619420,
%T A215859 2779264615127,111226656560877,4710924208619304,211105699482022215,
%U A215859 9997623229700175712,499562336689773070263,26288415481415803589236,1454007169289989503463230,84361156450441837460650255
%N A215859 Number of simple labeled graphs on n nodes with exactly 9 connected components that are trees or cycles.
%H A215859 Alois P. Heinz, <a href="/A215859/b215859.txt">Table of n, a(n) for n = 9..150</a>
%e A215859 a(10) = 45: each graph has one 2-node tree and 8 1-node trees and C(10,2) = 45.
%p A215859 T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
%p A215859       `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
%p A215859       `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
%p A215859     end:
%p A215859 a:= n-> T(n, 9):
%p A215859 seq(a(n), n=9..25);
%Y A215859 Column k=9 of A215861.
%Y A215859 The unlabeled version is A215989.
%K A215859 nonn
%O A215859 9,2
%A A215859 _Alois P. Heinz_, Aug 26 2012