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For the classical N-vector model, with arbitrary N, we have computed throughorder \beta^{17} the high temperature expansions of the second field derivativeof the susceptibility \chi_4(N,\beta) on the simple cubic and on the bodycentered cubic lattices. (The N-vector model is also known as the O(N)symmetric classical spin Heisenberg model or, in quantum field theory, as thelattice  O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) onthe two lattices, and by carefully allowing for the corrections to scaling, weobtain updated estimates of the critical parameters and more accurate tests ofthe hyperscaling relation d\nu(N) +\gamma(N) -2\Delta_4(N)=0 for a range ofvalues of the spin dimensionality N, including  N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model],  N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recentlyextended series for the susceptibility and for the second correlation moment,we also compute the dimensionless renormalized four point coupling constantsand some universal ratios of scaling correction amplitudes in fair agreementwith recent renormalization group estimates.Comment: 23 pages, latex, no figure

Renormalized couplings and scaling correction amplitudes in theN-vector spin models on the sc and the bcc lattices