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A215989 Number of simple unlabeled graphs on n nodes with exactly 9 connected components that are trees or cycles.

%I A215989 #7 Dec 04 2014 07:00:09
%S A215989 1,1,3,6,13,26,56,115,247,533,1174,2633,6031,14055,33343,80386,196569,
%T A215989 487017,1220491,3090331,7896160,20341323,52783053,137867631,362237861,
%U A215989 956881142,2540051927,6772828374,18133435767,48734282113,131434508449,355627568994
%N A215989 Number of simple unlabeled graphs on n nodes with exactly 9 connected components that are trees or cycles.
%H A215989 Alois P. Heinz, <a href="/A215989/b215989.txt">Table of n, a(n) for n = 9..650</a>
%e A215989 a(11) = 3: .o-o o o o o.  .o-o o o o o.  .o o o o o o.
%e A215989            .|/         .  .|          .  .| |        .
%e A215989            .o o o o o  .  .o o o o o  .  .o o o o o  .
%p A215989 with(numtheory):
%p A215989 b:= proc(n) option remember; local d, j; `if`(n<=1, n,
%p A215989       (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))
%p A215989     end:
%p A215989 g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-
%p A215989       (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2
%p A215989     end:
%p A215989 p:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,
%p A215989       `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*
%p A215989        p(n-i*j, i-1, t-j), j=0..min(n/i,t)))))
%p A215989     end:
%p A215989 a:= n-> p(n, n, 9):
%p A215989 seq(a(n), n=9..50);
%Y A215989 Column k=9 of A215977.
%Y A215989 The labeled version is A215859.
%K A215989 nonn
%O A215989 9,3
%A A215989 _Alois P. Heinz_, Aug 29 2012