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In an attempt to generalise knot matrix models for non-torus knots, whichcurrently remains an open problem, we derived formulas for the Harer-Zagiertransform of the HOMFLY-PT polynomial for some infinite families of twistedhyperbolic knots. Among them, we found a family of Pretzel knots for which thetransform has a fully factorised form, while for the remaining familiesconsidered it consists of sums of factorised terms. Their zeros have aremarkable structure as the modulus of their product always equals unity.

Harer-Zagier formulas for families of twisted hyperbolic knots