Formula to describe this sequence

I have a pattern of sequences that I want to define.
The first sequence is $2$. In the next sequence you double that to get $4$, put $6$, and then put $4$ again. In the third sequence you double the previous sequence to get $8,12,8$, write $6$, then write $8,12,8$. This pattern continues, doubling the last sequence, writing $6$, then rewriting the the first set of numbers, so we would have
$$2\\4,6,4\\8,12,8,6,8,12,8\\16,24,16,12,16,24,16,6,16,24,16,12,16,24,16$$

Is there a closed formula to represent the $k$th number in the $n$th row?

I also would like to know this answer when we start with $6$ as the first number so we have
$$6\\12,6,12\\24,12,24,6,24,12,24\\48,24,48,12,48,24,48,6,48,24,48,12,48,24,48$$

NOTE: I slightly edited my main question seconds before String answered, so his answer doesn't exactly reflect my question. I'm still looking for a better solution.