%I #8 Dec 04 2014 06:57:56
%S 1,36,1110,31680,904299,26603148,821278744,26864874465,935625630797,
%T 34750489933016,1375999952017938,57998361908305494,
%U 2596646585329104847,123180358220543885268,6175880603945440333627,326438846760992348696038,18147404450341079958539275
%N Number of simple labeled graphs on n nodes with exactly 8 connected components that are trees or cycles.
%H Alois P. Heinz, <a href="/A215858/b215858.txt">Table of n, a(n) for n = 8..150</a>
%e a(9) = 36: each graph has one 2-node tree and 7 1-node trees and C(9,2) = 36.
%p T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
%p `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
%p `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
%p end:
%p a:= n-> T(n, 8):
%p seq(a(n), n=8..25);
%Y Column k=8 of A215861.
%Y The unlabeled version is A215988.
%K nonn
%O 8,2
%A _Alois P. Heinz_, Aug 26 2012
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