We calculate the universal ratios R2k of renormalized coupling constants g2k entering the critical equation of state for the generalized Heisenberg (three-dimensional n-vector) model. Renormalization group (RG) expansions of R8 and R10 for arbitrary n are found in the four-loop and three-loop approximations respectively. Universal octic coupling R8 is estimated for physical values of spin dimensionality n=0,1,2,3 and for n=4,...64 to get an idea about asymptotic behavior of R8. Its numerical values are obtained by means of the resummation of the RG series and within the pseudo-ε expansion approach. Regarding R10 our calculations show that three-loop RG and pseudo-ε expansions possess big and rapidly growing coefficients for physical values of n what prevents getting fair numerical estimates.