  The high-temperature expansion coefficients of the ordinary and the higher
susceptibilities of the spin-1/2 nearest-neighbor Ising model are calculated
exactly up to the 20th order for a general d-dimensional (hyper)-simple-cubical
lattice. These series are analyzed to study the dependence of critical
parameters on the lattice dimensionality. Using the general $d$ expression of
the ordinary susceptibility, we have more than doubled the length of the
existing series expansion of the critical temperature in powers of 1/d.
