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If ${}^{20}C_1 + (2^2) \cdot {}^{20}C_2 + (3^2) \cdot {}^{20}C_3 + \ldots + (20^2) \cdot {}^{20}C_{20} = A(2^\beta)$, then $(A, \beta)$ is:
(1) $(420, 19)$ (2) $(420, 18)$ (3) $(380, 18)$ (4) $(380, 19)$
$\sum r^2 {}^{20}C_r = 20 \cdot 21 \cdot 2^{18} = 420 \times 2^{18}$.
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