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<DIV><FONT face=Arial size=2>Seqfans,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Let p be a partition of n.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Define Perm(p) to be the number of
permutations on p (if we consider p as a multiset) or equivalently the
number of compositions generated by p.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Then, it seems that </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>number of partitions p of n such that Perm(p)
is odd = <SPAN style="COLOR: black"><FONT size=3><FONT
face="Times New Roman">number of partitions of n into powers of 2 =
</FONT><FONT face=Arial size=2>A018819(n)
.</FONT></FONT></SPAN></FONT></DIV>
<DIV><FONT face="Times New Roman" size=3><SPAN
style="COLOR: black"></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN style="COLOR: black">Is there a (simple
bijective) proof of this conjecture?</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN
style="COLOR: black"></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN
style="COLOR: black"></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN style="COLOR: black">Best
regards,</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN
style="COLOR: black"></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN style="COLOR: black">Vladeta
Jovovic</SPAN></FONT></DIV></DIV></BODY></HTML>