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A215980 Number of simple unlabeled graphs on n nodes with exactly 10 connected components that are trees or cycles.

%I A215980 #7 Dec 04 2014 07:01:41
%S A215980 1,1,3,6,13,26,56,115,247,533,1175,2635,6037,14069,33378,80466,196759,
%T A215980 487453,1221515,3092719,7901816,20354765,52815434,137946253,362430959,
%U A215980 957359614,2541249138,6775848932,18141119582,48753971355,131485310625,355759469235
%N A215980 Number of simple unlabeled graphs on n nodes with exactly 10 connected components that are trees or cycles.
%H A215980 Alois P. Heinz, <a href="/A215980/b215980.txt">Table of n, a(n) for n = 10..650</a>
%e A215980 a(12) = 3: .o-o o o o o.  .o-o o o o o.  .o o o o o o.
%e A215980            .|/         .  .|          .  .| |        .
%e A215980            .o o o o o o.  .o o o o o o.  .o o o o o o.
%p A215980 with(numtheory):
%p A215980 b:= proc(n) option remember; local d, j; `if`(n<=1, n,
%p A215980       (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))
%p A215980     end:
%p A215980 g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-
%p A215980       (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2
%p A215980     end:
%p A215980 p:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,
%p A215980       `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*
%p A215980        p(n-i*j, i-1, t-j), j=0..min(n/i,t)))))
%p A215980     end:
%p A215980 a:= n-> p(n, n, 10):
%p A215980 seq(a(n), n=10..50);
%Y A215980 Column k=10 of A215977.
%Y A215980 The labeled version is A215860.
%K A215980 nonn
%O A215980 10,3
%A A215980 _Alois P. Heinz_, Aug 29 2012