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%I #7 Dec 04 2014 06:58:43
%S 1,1,3,6,13,26,56,115,247,532,1172,2627,6017,14020,33263,80196,196133,
%T 485993,1218103,3084686,7882748,20309036,52704689,137675229,361761187,
%U 955688561,2537043121,6765174365,18113821981,48683671360,131303094976,355284353448
%N Number of simple unlabeled graphs on n nodes with exactly 8 connected components that are trees or cycles.
%H Alois P. Heinz, <a href="/A215988/b215988.txt">Table of n, a(n) for n = 8..650</a>
%e a(10) = 3: .o-o o o o. .o-o o o o. .o o o o o.
%e .|/ . .| . .| | .
%e .o o o o o. .o o o o o. .o o o o o.
%p with(numtheory):
%p b:= proc(n) option remember; local d, j; `if`(n<=1, n,
%p (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))
%p end:
%p g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-
%p (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2
%p end:
%p p:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,
%p `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*
%p p(n-i*j, i-1, t-j), j=0..min(n/i,t)))))
%p end:
%p a:= n-> p(n, n, 8):
%p seq(a(n), n=8..50);
%Y Column k=8 of A215977.
%Y The labeled version is A215858.
%K nonn
%O 8,3
%A _Alois P. Heinz_, Aug 29 2012
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