%I #7 Dec 04 2014 07:12:41
%S 1,1,3,6,13,26,56,114,244,524,1152,2578,5902,13750,32637,78745,192755,
%T 478071,1199357,3039832,7774296,20043911,52049890,136041966,357650346,
%U 945253939,2510351950,6696412901,17935526721,48218592753,130083292745,352068892155
%N Number of simple unlabeled graphs on n nodes with exactly 6 connected components that are trees or cycles.
%H Alois P. Heinz, <a href="/A215986/b215986.txt">Table of n, a(n) for n = 6..650</a>
%e a(8) = 3: .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.
%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, 6):
%p seq(a(n), n=6..40);
%Y Column k=6 of A215977.
%Y The labeled version is A215856.
%K nonn
%O 6,3
%A _Alois P. Heinz_, Aug 29 2012