A (n, k) = 1 A (n-1, k-1) [+1]
           2 A (n-1, k-1) [+2]
           ...
           n A (n-1, k-1) [+n]


A (4, 3) = 1 A (3, 2) [+1]
           2 A (3, 2) [+2]
           3 A (3, 2) [+3]
           4 A (3, 2) [+4]

A (3, 2) = 1 2        A (3, 2) [+1] = 2 3     A (3, 2) [+2] = 1 3
           1 3                        2 4                     1 4
           2 1                        3 2                     3 1
           2 3                        3 4                     3 4
           3 1                        4 2                     4 1
           3 2                        4 3                     4 3