multi-index notatons

Question

I have two index $p_i^j$ where $i=1,2,\dots n$ and $j=1,2,\dots,\infty$, i.e the elements are $p_1^1,p_2^1,\dots,p_n^1$, $p_1^2,p_2^2,\dots,p_n^2$, $\dots$, could anyone tell me how to write them in a compact form? $\{p_i^j\}_{i=1}^{n}$ is not working. Thanks for helping.