Wikipedia gives the gain of an n-order Butterworth filter as
$$G^2(\omega)=\left |H(j\omega)\right|^2 = \frac {{G_0}^2}{1+\left(\frac{j\omega}{\omega_c}\right)^{2n}}$$
here. If you look at the gain at the cutoff frequency, the denominator becomes $(1+j^{2n})$, which blows up to infinity for odd $n$. Am I doing something wrong? Are Butterworth filters, or that formula, restricted to even $n$?