  Various formulas for currents with arbitrary spin are worked out in general
space-time dimension, in the free field limit and, at the bare level, in
presence of interactions. As the n-dimensional generalization of the
(conformal) vector field, the (n/2-1)-form is used. The two-point functions and
the higher-spin central charges are evaluated at one loop. As an application,
the higher-spin hierarchies generated by the stress-tensor operator-product
expansion are computed in supersymmetric theories. The results exhibit an
interesting universality.
