The $k$_th coefficient of the polynomial :$f_n(z)f_m(jz)+f_m(z)f_n(jz) $

Question

Let $j=e^{2i\pi/3}$ ( $i$ is the complex number $i^2=-1$), and let : $$f_n(z)=(1+z)^n$$

Question Is there an expression (without using sums) of the $k$_th coefficient of the following polynomial :$$f_n(z)f_m(jz)+f_m(z)f_n(jz) $$