2016/080)Find the coefficient $x^3$ in $1+ (1+x) + (1+x)^2 + (1+x)^3\cdots(1+x)^n$

we have $1+ (1+x) + (1+x)^2 + (1+x)^3\cdots(1+x)^n= \frac{(1+x)^{n+1} -1 }{1+x-1}$
$= \frac{(1+x)^{n+1} -1 }{x}$
so coeffient $x^3$ in $1+ (1+x) + (1+x)^2 + (1+x)^3\cdots(1+x)^n$ is coefficient of $x^4$ in $(1+x)^{n+1} -1$
or ${n+1 \choose 4}$