Khai triển \({{ \left( 1+2x+3{{x}^{2}} \right)}^{10}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{20}}{{x}^{20}}. \)Tính tổng \(S={{a}_{0}}+2{{a}_{1}}+4{{a}_{2}}+...+{{2}^{20}}{{a}_{20}}. \)
A. \(S={{15}^{10}}.\)
B. \(S={{17}^{10}}.\)
C. \(S={{7}^{10}}.\)
D. \(S={{7}^{20}}.\)