Nontrivial holomorphic vector bundle on $\mathbb{C}^n$

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Does there exist any nontrivial holomorphic vector bundle on $\mathbb{C}^n$?

I know $(1)$ Every line bundle on $\mathbb{C}^n$ is trivial, $(2)$ Every holomorphic vector bundle on $\mathbb{C}$ is trivial, (3) There exist a nontrivial line bundle on a contractible complex manifold, but I'm not sure if the above statement is true.