And Julia keeps amazing me: high precision computation

[danielwe]

    #          4 ⋅ (l - t + 1) ⋅ (p - t + 1) ⋅ (l - p - t + 1)
    #  k_t = - ─────────────────────────────────────────────── ⋅ k_{t - 1} ,
    #            t ⋅ (2l - 2t + 2) ⋅ (2l - 2t + 1) ⋅ sin(i)^2

Looks like the first parenthesized factors in the numerator and denominator cancel and return 1/2. Hence,

    #          2 ⋅ (p - t + 1) ⋅ (l - p - t + 1)
    #  k_t = - ───────────────────────────────── ⋅ k_{t - 1} ,
    #            t ⋅ (2l - 2t + 1) ⋅ sin(i)^2