  High temperature expansions for the free energy, the susceptibility and the
second correlation moment of the classical N-vector model [also denoted as the
O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear
sigma model] have been extended to order beta^{21} on the simple cubic and the
body centered cubic lattices, for arbitrary N. The series for the second field
derivative of the susceptibility has been extended to order beta^{17}. An
analysis of the newly computed series yields updated estimates of the model's
critical parameters in good agreement with present renormalization group
estimates.
