Relations Satisfied by Point Vortex Equilibria with Strength Ratio $-2$

Relations satisfied by the roots of the Loutsenko sequence of polynomials are derived. These roots are known to correspond to families of stationary and uniformly translating point vortices with two vortex strengths in ratio $-2$. The relations are analogous to those satisfied by the roots of the Adler–Moser polynomials, corresponding to equilibria with ratio $-1$. The proof uses an analysis of the differential equation that these polynomial pairs satisfy.