It's even worse, because the speed of factoring algorithms is measured against the number of digits of the binary expansion, and this is a unary expansion. So it's really O(2^n^2)
You really have to put parentheses when building "towers" of exponentials. The bound is (2^n)^2, which simplifies to 2^(2n). This is of course still horrible, but much less so than the 2^(n^2) for which what you wrote may be mistaken.
It's right associative, normally :)
Yeah, I realized that after the edit link expired. Let's just disambiguate the expression in whatever way makes me look best :)