If ${ }^{20} \mathrm{C}_1+\left(2^2\right)^{20} \mathrm{C}_2+\left(3^2\right)^{20} \mathrm{C}_3+\ldots \ldots . .+\left(20^2\right)^{20} \mathrm{C}_{20}=\mathrm{A}\left(2^\beta\right)$, then the ordered pair $(\mathrm{A}, \beta)$ is equal to:
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