On Manin's conjecture for a certain singular cubic surface
  Let U denote the open subset formed by deleting the unique line from the singular cubic surface x_1x_2^2+x_2x_0^2+x_3^3=0. In this paper an asymptotic formula is obtained for the number of rational points on U of bounded height, which thereby verifies the Manin conjecture for this particular surface. 
R. de la Breteche, T.D. Browning and U. Derenthal