  We extend the definition of the refined topological vertex C to an n-coloured
refined topological vertex C_n that depends on n free bosons, and compute the
5D strip partition function made of N pairs of C_n vertices and conjugate C*_n
vertices. Using geometric engineering and the AGT correspondence, the 4D limit
of this strip partition function is identified with a (normalized) matrix
element of a (primary state) vertex operator that intertwines two (arbitrary
descendant) states in a (generically non-rational) 2D conformal field theory
with Z_n parafermion primary states.
