  We present a differential formulation of the recursion formula of the
hierarchical model which provides a recursive method of calculation for the
high-temperature expansion. We calculate the first 30 coefficients of the high
temperature expansion of the magnetic susceptibility of the Ising hierarchical
model with 12 significant digits. We study the departure from the approximation
which consists of identifying the coefficients with the values they would take
if a $[0,1]$ Pad\'e approximant were exact. We show that, when the order in the
high-temperature expansion increases, the departure from this approximation
grows more slowly than for nearest neighbor models. As a consequence, the value
of the critical exponent $\gamma $ estimated using Pad\'e approximants
converges very slowly and the estimations using 30 coefficients have errors
larger than 0.05. A (presumably much) larger number of coefficients is
necessary to obtain the critical exponents with a precision comparable to the
precision obtained for nearest neighbor models with less coefficients. We also
discuss the possibility of constructing models where a $[0,1]$ Pad\'e
approximant would be exact.
