  We give combinatorial formulae for vector-valued weight functions (off-shell
nested Bethe vectors) for tensor products of irreducible evaluation modules
over the Yangian $Y({\mathfrak{gl}}_N)$ and the quantum affine algebra
$U_q(\widetilde{{\mathfrak{gl}}_N})$.
  The results of the paper were obtained in 1998 and were used in
math.QA/9905137, math.QA/0302148, math.QA/0610517.
