Let $1(n)$ be the number of digits $1$ in binary representation of number $n$.

For example, $13=1101_2$ so $1(13)=3\\$

Is there explicit form of $\,\,\sum{1(i)x^i} $?

I checked OEIS and didn't find information about this sequence (1,1,2,2,2,3,1,2,2,3,...)