A047060 Array T read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no step touches the line y=5x/3 unless x=0 or x=h.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 3, 2, 5, 4, 1, 1, 4, 3, 7, 9, 5, 1, 1, 5, 7, 7, 16, 14, 6, 1, 1, 6, 12, 14, 23, 30, 20, 7, 1, 1, 7, 18, 12, 37, 53, 50, 27, 8, 1, 1, 8, 25, 30, 37, 90, 103, 77, 35, 9, 1, 1, 9, 33, 55, 30, 127, 193, 180, 112