FUNCTION:  partitions[POE] - OE(n)
 
CALLING SEQUENCE:  POE(n)
 
PARAMETERS:     n  -  positive integer
 
SYNOPSIS:  
   POE(n) computes OE(n) (hard way). This is the number of partitions of
   n in which every even part is below each odd part.
                    
EXAMPLES:  
                    
> with(qseries):
> with(partitions):
> POE(12);
                                       30

> GENFUNC:=1+add(POE(n)*q^n,n=1..10);
GENFUNC :=

        10       9       8      7      6      5      4      3      2
    19 q   + 12 q  + 12 q  + 7 q  + 7 q  + 4 q  + 4 q  + 2 q  + 2 q  + q + 1

> prodmake(GENFUNC,q,10);
                                       1
                -----------------------------------------------
                           2         4         6         8
                (1 - q) (-q  + 1) (-q  + 1) (-q  + 1) (-q  + 1)

DISCUSSION:  
   OE(12) = 30 and the generating function seems like a nice
   product
                    
SEE ALSO:  ptnOE