This sum is written in my Galois Theory notes. Surely if $a_{{i_1}{i_1}...{i_t}} $ then the $i_1$'s would just infinitely repeat, along with the $i_2$'s, etc. This notation just doesn't compute with my brain and I'm wondering if my lecturer meant to write $a_{{i_1}{i_2}...{i_t}}$ but he defines $0 \le i \le t$ so surely this covers it, and the indexes $i_1 , i_2 ,...$ are redundant.