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${}^2C_2 = {}^3C_3$. $S = {}^3C_3 + {}^4C_3 + \ldots + {}^nC_3 = {}^{n+1}C_4$. The value of $\frac{n(n+1)(2n+1)}{6}$ is ____.
Using hockey stick identity and solving, the answer is 12.
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