1-Loop Approximation for Fermionic Effective Action

Given a partition function

$$
Z = int mathscr{D}(bar{psi}, psi) , mathrm{exp} left( , – S[bar{psi}, psi] right)
$$

with fermionic (Grassmann) fields. I seek to calculate the effective action $Gamma[bar{Psi}, Psi]$ within the one-loop approximation. The formula should read

$$
Gamma [bar{Psi}, Psi] approx S [bar{Psi}, Psi] – operatorname{tr} operatorname{log} S^{2} [bar{Psi}, Psi]
$$

Question: What is $ S^{2} [bar{Psi}, Psi] $?

In my logic it should be

$$
S^{2} [bar{Psi}, Psi] = frac{delta^2}{delta bar{psi} delta psi} S[bar{psi}, psi] bigg vert_{psi = Psi}
$$

(with additional arguments added to the functional derivatives of the fields…) It confuses me that I saw a different formula for the bosonic counterpart; Can anybody recommend some literature with a derivation?