This note outlines the steps for proving that the moments of a randomly-selected subset of a general ETF (complex, with aspect ratio $0<gamma<1$) converge to the corresponding MANOVA moments. We bring here an extension for the proof of the Kesten-Mckay moments (real ETF, $gamma=1/2$) cite{magsino2020kesten}. In particular, we establish a recursive computation of the $r$th moment, for $r = 1,2,ldots$, and verify, using a symbolic program, that the recursion output coincides with the MANOVA moments.
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