Series Expansion of $(e^{(-\lambda/\mu_A}) \mu_A)/ (E_{-k_1} (\lambda/\mu_A))$ at $\lambda \to \infty$

Question

I would like to find the series expansion of $$\mu_A\frac{e^{-\lambda/\mu_A} }{ E_{-k_1} (\lambda/\mu_A)} \quad \text{as} \,\, \lambda \to \infty$$ . Mathematica calculates it as: $\lambda - k_1 \mu_A + (k_1 \mu_A^2)/\lambda$ but I cannot validate it. $E_{-k_1} (\lambda/\mu_A)$ is the exponential integral.

I would really appreciate the help!