Complex interpolation of Orlicz sequence spaces and its higher order Rochberg spaces

We show that if $({\mathrm{\ell }}_{{\varphi }_0},{\mathrm{\ell }}_{{\varphi }_1})$ is a couple of suitable Orlicz sequence spaces then the corresponding Rochberg derived spaces of all orders associated to the complex interpolation method are Fenchel-Orlicz spaces. In particular, the induced twisted sums have the $(C[0, 1], $\mathbb{C}$)$-extension property.