Coefficient of $x^k$ in expansion of $(1+x)(1+x+x^2)(1+x+x^2+x^3)\cdots(1+x+x^2+x^3+\ldots+x^n)$ under modulo 2?

Question

Is there any general formula for finding coefficient of $x^k$ in $(1+x)(1+x+x^2)(1+x+x^2+x^3)\cdots(1+x+x^2+x^3+\ldots+x^n)$ under modulo 2?