Energy eigenvalues and 〈*x*^{2}〉_{n} for the oscillators having potential energy*V*(*x*)=(*ω*^{2}*x*^{2}/2)+*λ*<*x*^{2r}>*x*^{2s} have been determined for various values of*λ, r, s* and*n* using renormalized hypervirial-Padé scheme. In general, the results show an improvement over the findings of earlier workers. Variation of the evaluated quantities and of the renormalization parameter with*λ, r, s* and*n* has been discussed. In addition, this potential has been employed as an illustrative example of the applicability of alternative formalism of perturbation theory developed by Kim and Sukhatme (*J. Phys.**A25* 647 (1992)).