A047040 - OEIS

A047040

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=3x/4 unless x=0 or x=h.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 4, 5, 2, 3, 1, 1, 5, 9, 5, 5, 4, 1, 1, 6, 14, 14, 10, 9, 5, 1, 1, 7, 20, 28, 14, 9, 14, 6, 1, 1, 8, 27, 48, 42, 14, 23, 20, 7, 1, 1, 9, 35, 75, 90, 56, 23, 43, 27, 8, 1, 1, 10, 44, 110, 165, 146, 56, 66, 70, 35