n :  parenthesizations P(n)
  1 :  1
  2 :  1
  3 :  2
  4 :  5
  5 :  14
  6 :  42
 10 :  4862
 15 :  2674440
 20 :  1767263190
 25 :  1289904147324

Same answer, three implementations, on random chains:

n    answer      plain calls   plain ms    memo calls    memo ms     bottom ms   
4    15596       27            0.000       21            0.000       0.003       
8    3839        2187          0.006       169           0.001       0.001       
12   16508       177147        0.501       573           0.002       0.003       
15   62862       4782969       12.033      1121          0.004       0.004       
17   14523       43046721      109.037     1633          0.005       0.006       
60   44364       (not run)     -           71981         0.208       0.076       
200  143061      (not run)     -           2666601       6.834       1.601
