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A215987 Number of simple unlabeled graphs on n nodes with exactly 7 connected components that are trees or cycles.

%I A215987 #8 Dec 04 2014 06:57:25
%S A215987 1,1,3,6,13,26,56,115,246,530,1166,2613,5982,13940,33073,79760,195109,
%T A215987 483615,1212485,3071358,7850690,20231286,52513864,137202595,360578812,
%U A215987 952705531,2529454122,6745724961,18063628118,48553319703,130962595786,354390168855
%N A215987 Number of simple unlabeled graphs on n nodes with exactly 7 connected components that are trees or cycles.
%H A215987 Alois P. Heinz, <a href="/A215987/b215987.txt">Table of n, a(n) for n = 7..650</a>
%e A215987 a(9) = 3: .o-o o o o.  .o-o o o o.  .o o o o o.
%e A215987           .|/       .  .|        .  .| |      .
%e A215987           .o o o o  .  .o o o o  .  .o o o o  .
%p A215987 with(numtheory):
%p A215987 b:= proc(n) option remember; local d, j; `if`(n<=1, n,
%p A215987       (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))
%p A215987     end:
%p A215987 g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-
%p A215987       (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2
%p A215987     end:
%p A215987 p:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,
%p A215987       `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*
%p A215987        p(n-i*j, i-1, t-j), j=0..min(n/i,t)))))
%p A215987     end:
%p A215987 a:= n-> p(n, n, 7):
%p A215987 seq(a(n), n=7..50);
%Y A215987 Column k=7 of A215977.
%Y A215987 The labeled version is A215857.
%K A215987 nonn
%O A215987 7,3
%A A215987 _Alois P. Heinz_, Aug 29 2012