  With the help of the evolution method we calculate all HOMFLY polynomials in
all symmetric representations [r] for a huge family of (generalized) pretzel
links, which are made from g+1 two strand braids, parallel or antiparallel, and
depend on g+1 integer numbers. We demonstrate that they possess a pronounced
new structure: are decomposed into a sum of a product of g+1 elementary
polynomials, which are obtained from the evolution eigenvalues by rotation with
the help of rescaled SU_q(N) Racah matrix, for which we provide an explicit
expression. The generalized pretzel family contains many mutants,
undistinguishable by symmetric HOMFLY polynomials, hence, the extension of our
results to non-symmetric representations R is a challenging open problem. To
this end, a non-trivial generalization of the suggested formula can be
conjectured for entire family with arbitrary g and R.
