Abstract: More stable and accurate recursive formulas and a computing procedure to calculate scattering coefficients for a multilayered sphere are proposed. The procedure involves three logarithmic derivatives of Ricatti-Bessel functions 'n(z)/n(z), 'n(z)/n(z),'n(z)/n(z), as well as the ratio n(z)/n(z). The asymptotic behavior, stability, and accuracy of the procedure and scattering coefficients an, and bn are discussed for various complex refractive indices. This procedure can be applied to large and small inhomogeneous spherical particles.