A095268 Graphical Partitions - Extend?

[franktaw at netscape.net]

Two points, neither answering Paul's questions.

The comment in A095268 could be improved.  Instead of "the number of 
these graphs having distinct degree sequences", it should read 
something like "the number of distinct degree sequences these graphs 
possess".  If two graphs have the same degree sequence, then neither of 
them has a _distinct_ degree sequence; but we do want to count that 
degree sequence once.

Second, as I'm sure Paul knows, a sequence has a self-convolution 
sequare-root iff all the odd-index terms are even.  So far, A095268 has 
a strict alternation of parity.  Does that continue?

Franklin T. Adams-Watters


-----Original Message-----
From: Paul D. Hanna <pauldhanna at juno.com>

Seqfans,
     Could someone extend sequence: A095268
"Numbers of distinct graphical partitions corresponding to graphs on 
n=1,
2, ... nodes."

With offset 0, A095268 begins:
[0, 0, 1, 2, 7, 20, 71, 240, 871, 3148, ?]

The self-convolution square-root of A095268 (with offset 0) begins:
B = [0, 1, 1, 3, 7, 24, 75, 264, 917, ?]

I wonder ... do the terms of B continue to be integer?

Since a g.f. for A095268 is not known, it would be interesting
if the trend continued for more terms.

More information may be found at:
http://mathworld.wolfram.com/GraphicalPartition.html
http://www.mathe2.uni-bayreuth.de/axel/

Thanks,
     Paul