Sequence space representations for spaces of entire functions with rapid decay on strips

We obtain sequence space representations for a class of Fr\'echet spaces of entire functions with rapid decay on horizontal strips. In particular, we show that the projective Gelfand-Shilov spaces $\Sigma^1_\nu$ and $\Sigma^\nu_1$ are isomorphic to $\Lambda_{\infty}(n^{1/(\nu+1)})$ for $\nu > 0$.