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A215988 Number of simple unlabeled graphs on n nodes with exactly 8 connected components that are trees or cycles.

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