Number of lattice paths from (0,0) to (n,0) that do not go below the x-axis and consist of steps U=(1,1), D=(1,-1) and H=(1,0), where H-steps are only allowed if y=1.

A224747

Number of lattice paths from (0,0) to (n,0) that do not go below the x-axis and consist of steps U=(1,1), D=(1,-1) and H=(1,0), where H-steps are only allowed if y=1.