  We study proper lattice animals for bond- and site-percolation on the
hypercubic lattice $\mathbb{Z}^d$ to derive asymptotic series of the
percolation threshold $p_c$ in $1/d$, The first few terms of these series were
computed in the 1970s, but the series have not been extended since then. We add
two more terms to the series for $\pcsite$ and one more term to the series for
$\pcbond$, using a combination of brute-force enumeration, combinatorial
identities and an approach based on Pad\'e approximants, which requires much
fewer resources than the classical method. We discuss why it took 40 years to
compute these terms, and what it would take to compute the next ones. En
passant, we present new perimeter polynomials for site and bond percolation and
numerical values for the growth rate of bond animals.
