Let $(\mathcal A,\varphi)$ be a tracial algebraic noncommutative probability space, and let $(a_i)_{i\in\mathbb N}$ be a freely independent sequence of identically distributed self-adjoint elements of $\mathcal A$ such that $\varphi(a_1)=0$ and $\varphi(a_1^2)=1$. For each $n\in\mathbb N$, define
Then $(S_n)_{n\in\mathbb N}$ converges in noncommutative distribution, equivalently in all moments, to a standard semicircular element $s$, characterized by free cumulants
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\begin{align*}
\kappa_1(s)=0,\qquad \kappa_2(s,s)=1,\qquad \kappa_m(s,\dots,s)=0\quad\text{for every }m\geq 3.
\end{align*}