Deep Binomials

For $$r = 0, 1, ..., 10,$$ let $$A_{r}$$, $$B_{r}$$ and $$C_{r}$$ denote, respectively, the coefficient of $$x^{r}$$ in the expansions of $$(1+x)^{10}$$, $$(1+x)^{20}$$ and $$(1+x)^{30}$$. Then $$\sum\limits_{r=1}^n A_{r}(B_{10}B_{r} - C_{10}A_{r})$$ is equal to

Note: Take $$n = 10$$.

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