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<DIV>Seqfans, </DIV>
<DIV> </DIV>
<DIV>Someone wrote: <BR>> Since you are given as the reference for the
(2), I wonder how you <BR>> came up with it. </DIV>
<DIV> </DIV>
<DIV>I was interested back then in documenting recursive equations </DIV>
<DIV>that seem to occur in nature, and so perhaps I found that A000621 </DIV>
<DIV>agreed with 40 initial terms of the equation A(x) = 1/(1 - x*A(x^2)).
</DIV>
<DIV>In retrospect, I should have indicated "conjecture" next to the g.f.
</DIV>
<DIV>since even 40 initial terms is not enough to be certain. </DIV>
<DIV> </DIV>
<DIV>> (without seeing the original references, your gf seems <BR>>
more plausible, because of the recursive nature of the original <BR>>
combinatorial situation, but who knows :) )</DIV>
<DIV> </DIV>
<DIV>Agreed - the recursive equation is most likely; an opinion supported
by </DIV>
<DIV>the g.f. for the closely related sequence A000625: </DIV>
<DIV>G.f. satisfies A(x) = 1 + x*(A(x)^3 + 2*A(x^3))/3. <BR> </DIV>
<DIV>As Neil suggested, I e-mailed Bruce Corrigan for possible clarification.
</DIV>
<DIV>Thanks to all for your comments.</DIV>
<DIV> </DIV>
<DIV>Regards,</DIV>
<DIV> Paul<BR></DIV></DIV></BODY></HTML>