Symplectic form and wedge sum

Question

The wedge sum of $k$ symplectic 2-forms is given by ( if $\omega = \sum_i e_i^* \wedge f_i^*$)

$$ \omega^k = k! \sum_{1\le i_1 <...<i_k \le n} (e_{i_1}^* \wedge f_{i_1}^*) \wedge ... \wedge (e_{i_k}^* \wedge f_{i_k}^*).$$

But now I read that $\omega^n(e_1,f_1,...,e_n,f_n)=1.$ This does not make sense to me, afais the result is $\omega^n(e_1,f_1,...,e_n,f_n)= n!$

Edit: Sorry, it was kind of stupid to me to not include the reference, but I wanted to ask this question and forgot where I saw it. But it was actually an answer here on math.stackexchange click me.

Answer 1

There's a reason $\dfrac{\omega^n}{n!}$ shows up all over complex geometry as the induced volume form. You are correct and there is an error in whatever you're reading.