$ python3 solver.py

printDp(20)

[[   1    0    0    0    0    0    0    0    0    0    0    0    0    0]
 [   2    1    0    0    0    0    0    0    0    0    0    0    0    0]
 [   3    3    0    0    0    0    0    0    0    0    0    0    0    0]
 [   2    6    2    0    0    0    0    0    0    0    0    0    0    0]
 [   1    7    7    1    0    0    0    0    0    0    0    0    0    0]
 [   0    6   14    6    0    0    0    0    0    0    0    0    0    0]
 [   0    3   18   18    3    0    0    0    0    0    0    0    0    0]
 [   0    1   16   34   16    1    0    0    0    0    0    0    0    0]
 [   0    0   10   45   45   10    0    0    0    0    0    0    0    0]
 [   0    0    4   43   84   43    4    0    0    0    0    0    0    0]
 [   0    0    1   30  113  113   30    1    0    0    0    0    0    0]
 [   0    0    0   15  114  208  114   15    0    0    0    0    0    0]
 [   0    0    0    5   87  285  285   87    5    0    0    0    0    0]
 [   0    0    0    1   50  300  518  300   50    1    0    0    0    0]
 [   0    0    0    0   21  246  720  720  246   21    0    0    0    0]
 [   0    0    0    0    6  157  786 1296  786  157    6    0    0    0]
 [   0    0    0    0    1   77  683 1823 1823  683   77    1    0    0]
 [   0    0    0    0    0   28  474 2052 3254 2052  474   28    0    0]
 [   0    0    0    0    0    7  261 1872 4625 4625 1872  261    7    0]
 [   0    0    0    0    0    1  112 1391 5344 8196 5344 1391  112    1]]