If `n` is a positive integer, find the coefficient of `x^(-1)` in the expansion of `(1+x)^n(1+1/x)^ndot`

Explanation

We have
`(1+x)^(n) (1+1/x)^(n) = (1+x)^(n) xx (1+x)^(n)/x^(n)= ((1+x)^(2n))/(x^(n))`.
Coefficent of `x^(-1) " in the expansion of "(1+x)^(n) (1+1/x)^(n)`
= coefficents of ` " coefficent of "x^(-1)" in the expansion of " ((1+x)^(2n))/(x^(n))`
`=" coefficent of" (x^(-1) xx x^(n)) " in the expansion of " (1+x)^(2n).`
`="coefficent of " x^(n-1) " in the expansion of " (1+x)^(2n)`
`.^(2n)C_(n-1)" "[:'(1+x)^(2n)= overset (2n)underset (r=0) sum.^(2n)C_(r)x^(r)].`