  We have derived long series expansions of the percolation probability for
site, bond and site-bond percolation on the directed triangular lattice. For
the bond problem we have extended the series from order 12 to 51 and for the
site problem from order 12 to 35. For the site-bond problem, which has not been
studied before, we have derived the series to order 32. Our estimates of the
critical exponent $\beta$ are in full agreement with results for similar
problems on the square lattice, confirming expectations of universality. For
the critical probability and exponent we find in the site case: $q_c =
0.4043528 \pm 0.0000010$ and $\beta = 0.27645 \pm 0.00010$; in the bond case:
$q_c = 0.52198\pm 0.00001$ and $\beta = 0.2769\pm 0.0010$; and in the site-bond
case: $q_c = 0.264173 \pm 0.000003$ and $\beta = 0.2766 \pm 0.0003$. In
addition we have obtained accurate estimates for the critical amplitudes. In
all cases we find that the leading correction to scaling term is analytic,
i.e., the confluent exponent $\Delta = 1$.
