  We use very efficient algorithms to calculate low-density series for bond and
site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$
lattices. Analysis of the series yields accurate estimates of the critical
point $p_c$ and various critical exponents. The exponent estimates differ only
in the $5^{th}$ digit, thus providing strong numerical evidence for the
expected universality of the critical exponents for directed percolation
problems. In addition we also study the non-physical singularities of the
series.
