If ^20C_1 + (2^2)^20C_2 + (3^2) ^20C_3 + ..... + (20^2)^20C_20 = A(2^β), then the ordered pair (A, β) is equal to

Correct option is A (420,18)(1+x)n=nC0+nC1x+nC2x2++nCDiff. w.r.t.x⇒n(1+x)n−1;=nC1+nC2(2x)++nCnn(Multiply byxboth side⇒nx(1+x)n−1;=nC1x+nC2(2x2)++nCnDiff w.r.t.x⇒n[(1+x)n−1;+(n−1;)x(1+x)n−2;]=nC1+nC222x+...nCn(Putx=1andn=20⇒20C1+22 20C2+32 20C3++20=20×218[2+19]=420(218)=A(2β.By comparing we getA=420,β=18