L^−1 {1 − e^−s/s(1 − e^−2s)} = ?
With CB's simplification re-write as
$\displaystyle
\mathcal{L}^{-1}\left[
\frac{1}{s(1+e^{-s})}
\right] =
\mathcal{L}^{-1}\left[
\frac{1}{s} - \frac{e^{-s}}{s} + \frac{e^{-2s}}{s} - \frac{e^{-3s}}{s} \pm \cdots
\right]
$
The inverse Laplace transform of each gives a series of step functions and together a square wave.