I'm trying to found a way how to prove this language is not context free. Using pumping lemma I'm halfway done. Consider word $a^{n^2}b^n$. If you divide it into $uvwxy$ and have only $a$'s in $v$ and $x$, you clearly get out of language when you pump up. If you do the same with $b$'s and pump down, you get out of language as well. But how dow do you show situation where there are only $a$'s in $v$ and just $b$'s in $x$?
Thank you