FUNCTION:  partitions[PDP] - Number of partitions of n (hard way)
 
CALLING SEQUENCE:  PDP(n)
 
PARAMETERS:      n -  nonnegative integer
 
GLOBAL VARIABLES:                     
SYNOPSIS:  
  PDP(n)   computes p(D,n) the hard way (by counting a list of partitions)
  p(D,n) is the number of partitions of n into distinct parts
                    
EXAMPLES:  
                    
> with(qseries):
> with(partitions):
> PDP(9);
                                       8

> series(etaq(q,2,12)/etaq(q,1,12),q,11);
          2      3      4      5      6      7      8      9       10      11
 1 + q + q  + 2 q  + 2 q  + 3 q  + 4 q  + 5 q  + 6 q  + 8 q  + 10 q   + O(q  )

DISCUSSION:  
   We see that p(D,9) = 8.
   Confirmed from the generating function
                    
SEE ALSO:  ptnDP