It is known that the sequence $\{a_n\}$ satisfies $a_1=2$, $a_n=2^{2n}a_{n-1}+n\cdot 2^{n^2}$, $(n \ge 2)$, find the general term of $a_n$.
Source: China Northern MO 2010 p1 CNMO
Tags: algebra, Sequence, recurrence relation
It is known that the sequence $\{a_n\}$ satisfies $a_1=2$, $a_n=2^{2n}a_{n-1}+n\cdot 2^{n^2}$, $(n \ge 2)$, find the general term of $a_n$.