I want to compute $\mathrm{Ext}_{\mathbb{Z}}^1 (\mathbb{Z}[[ t ]] , \mathbb{Z})$. By a classical result of Baer, the formal power series group $\mathbb{Z}[[ t ]]$ is not projective, so at first glance I do not have any reason to assume that the Ext group should vanish.
Any help is welcome.