  Renormalized coupling constants g_{2k} that enter the critical equation of
state and determine nonlinear susceptibilities of the system possess universal
values g*_{2k} at the Curie point. They are calculated, along with the ratios
R_{2k} = g_{2k}/g_4^{k-1}, for the three-dimensional scalar \lambda\phi^4 field
theory within the pseudo-\epsilon-expansion approach.
Pseudo-\epsilon-expansions for g*_6, g*_8, R*_6, and R*_8 are derived in the
five-loop approximation, numerical estimates are presented for R*_6 and R*_8.
The higher-order coefficients of the pseudo-\epsilon-expansions for the sextic
coupling are so small that simple Pade approximants turn out to be sufficient
to yield very good numerical results. Their use gives R*_6 = 1.650 while the
most recent lattice estimate is R*_6 = 1.649(2). For the octic coupling
pseudo-\epsilon-expansions are less favorable from the numerical point of view.
Nevertheless, Pade-Borel resummation leads in this case to R*_8 = 0.890, the
number differing only slightly from the values R*_8 = 0.871, R*_8 = 0.857
extracted from the lattice and field-theoretical calculations.
