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%I #9 Dec 04 2014 06:56:06
%S 1,21,434,8694,183099,4138827,101682724,2726328033,79746709042,
%T 2537322057270,87447979819018,3249640607490732,129613729260208069,
%U 5525005710150786189,250709547490889697735,12067446246711780717009,614138343777115783675203
%N Number of simple labeled graphs on n nodes with exactly 6 connected components that are trees or cycles.
%H Alois P. Heinz, <a href="/A215856/b215856.txt">Table of n, a(n) for n = 6..145</a>
%e a(7) = 21: each graph has one 2-node tree and 5 1-node trees and C(7,2) = 21.
%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, 6):
%p seq(a(n), n=6..25);
%Y Column k=6 of A215861.
%Y The unlabeled version is A215986.
%K nonn
%O 6,2
%A _Alois P. Heinz_, Aug 26 2012
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