Series expansion of the percolation threshold on hypercubic lattices

We study proper lattice animals for bond- and site-percolation on the hypercubic lattice \mathbb{Z}^dto derive asymptotic series of the percolation threshold p_cin 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 \pcsiteand one more term to the series for \pcbond using a combination of brute-force enumeration, combinatorial...