  In this paper, the results of part I regarding a special case of Feynman
identity are extended. The sign rule for a path in terms of data encoded by its
word and formulas for the numbers of distinct equivalence classes of
nonperiodic paths of given length with positive or negative sign are obtained
for this case. Also, a connection is found between these numbers and the
generalized Witt formula for the dimension of certain graded Lie algebras.
Convergence of the infinite product in the identity is proved.
