[seqfan] A000081 & nonoverlapping circles(?)

[r.shepherd]

Can anyone confirm that this comment in A81 below is correct?
Trying to see it for myself I've created a .jpg file that shows
25 arrangements of 5 nonoverlapping circles -- not A000081(6)=20.
When I asked Neil about this about 11 months ago, he said that
he believed the comment was correct but that he didn't have time
to double-check -- I'm only now getting back to it myself.

I'll be glad to send my .jpg file for (temporary) display by someone
who can link to it.  (I have no web page.).  Perhaps there needs to
be clarification of how to count these nonoverlapping circles -- or
I may just be counting some arrangements twice but I still don't
see it.  (I'm only counting arrangements in one plane or there'd be
lots more (and lots more confusion on how to count)....).

I find 1,1,2,4,9,25, which is not in the OEIS.
(There are 91 sequences in the OEIS with 1,1,2,4,9).

Thanks,
Rick

%I A000081 M1180 N0454
%S A000081 0,1,1,2,4,9,20,48,115,286,719,1842,4766,12486,32973,87811,235381,
%T A000081
634847,1721159,4688676,12826228,35221832,97055181,268282855,743724984,
%U A000081
2067174645,5759636510,16083734329,45007066269,126186554308,354426847597
%N A000081 Rooted trees with n nodes (or connected functions with a fixed
point).
%C A000081 Number of ways of arranging n-1 nonoverlapping circles: e.g.
there are 4 ways to arrange 3 circles, as repre\
  sented by ((O)), (OO), (O)O, OOO. (Of course the rules here are different
from the usual counting parentheses problem\
  s - compare A000108, A001190, A001699.)
<many lines omitted for brevity -- RS>