More stable and accurate recursive formulas and a computing procedure for scattering coefficient calculation of a multilayered sphere are proposed. This procedure involves three logarithmic derivatives of Ricatti-Bessel function $$\psi '_n (z)/\psi _n (z),\chi '_n (z)/\chi _n (z),\xi '_n (z)/\xi _n (z)$$ , as well as the ratio ψ n (z)/χ n (z). The asymptotic behavior, stability, and accuracy of the procedure and scattering coefficienta n andb n are discussed for various complex refractive indices. This procedure can be applied to large and small inhomogeneous spherical particles.