$ 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]]