Jelly, 7 bytes

×_’ 2Ç¡ 

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Uses this relationship provided in the sequence instead: a(n+1) = a(n)^2 - a(n) + 1

Jelly, 7 bytes

²_’ 2Ç¡ 

Try it online!

Uses this relationship provided in the sequence instead: a(n+1) = a(n)^2 - a(n) + 1

Explanation

2Ç¡ Main chain, argument in input 2 Start with 2 ¡ Repeat as many times as the input: Ç the helper link. ²_’ Helper link, argument: z ² z² ’ z - 1 _ subtraction, yielding z² - (z-1) = z² - z + 1