Limits Continuity And Differentiability

If \(\lim _\limits{x \rightarrow 0} \frac{a x^2 e^x-b \log _e(1+x)+c x e^{-x}}{x^2 \sin x}=1\), then \(16\left(a^2+b^2+c^2\right)\) is equal to ________.