Let $(\mathcal A,\varphi)$ be a noncommutative probability space, and let $(a_j)_{j \in \mathbb N}$ be freely independent and identically distributed elements of $\mathcal A$. For each $n \in \mathbb N$, define
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\begin{align*}
S_n := \frac{a_1+\cdots+a_n}{\sqrt n} \in \mathcal A.
\end{align*}
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Then, for every $m \in \mathbb N$ and every $n \in \mathbb N$, the $m$-th free cumulant satisfies