The coefficient of xn in the polynomial x+nC0x+3 nC1x+5 nC2…....x+(2n+1) nCn is

There are total (n + 1) factors, Iet P(x) = 0  Let x+nC0x+3nC1x+5nC2….....x+(2n+1) nCn=anxn+an−1xn−1+…+a1x+a0clearly , αn = 1 and roots of the equation P(x) = 0 are −nC0,−3nC1,…Sum of the roots = −an−1/an=−nC0−3nC1−5nC2⋯⇒ an−1=(n+1)2n