For a scalar field theory one introduces the partition function with external sources
$$ Z[j] = \int \mathscr{D} \varphi \, \exp \left( -S[\varphi] + \int j \, \varphi \right) \text{,} $$
the analogon of the free energy
$$ F[j] = \ln Z[j] \text{,} $$
and for the mapping
\begin{alignat}{2} C^{\infty}(\mathbb{R}^D) & \longrightarrow \, & C^{\infty}(\mathbb{R}^D) \\ j(\bullet) & \longmapsto & \frac{\delta}{\delta \, j(\bullet)} F[j] = \langle \varphi (\bullet) \rangle =: \phi[j] (\bullet) \end{alignat}
we denote with $j[\phi]$ the formal inverse mapping and define the effective action as
$$ \Gamma[\phi] = - F[j[\phi]] + \int \phi \, j[\phi] \text{.} $$
I seek to calculate the effective action $\Gamma^{4}$ (within first order perturbation theory) for a fermionic field theory with an action that is quartic in the (Grassmann-)fields.
Peskin, Schwartz, Altland and Coleman (my "standard-literature") don't seem to help.