Formulas for recurrence coefficients of orthogonal polynomials related to Lorentzian-like weights

One considers the recurrence relation of orthogonal polynomials related to weights |t|A(1+t2r/c2r)-B|t|A(1+t2r/c2r)-B on the whole real line, for various integer exponents 2r2r, and real A>-1A>-1, B>0B>0.