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a_n=2^{2n}a_{n-1}+n\cdot 2^{n^2}, a_1=2

Source: China Northern MO 2010 p1 CNMO

May 4, 2024
algebraSequencerecurrence relation

Problem Statement

It is known that the sequence {an}\{a_n\} satisfies a1=2a_1=2, an=22nan−1+n⋅2n2a_n=2^{2n}a_{n-1}+n\cdot 2^{n^2}, (n≥2)(n \ge 2), find the general term of ana_n.
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