I've already vaguely given you the answer

Algebra Level 5

Let g(x)g(x) denote a quintic (5th\big(5^\text{th}-degree)\big) polynomial such that g(n)=2ng(n) = 2^n for n=1,2,3,4,5n = 1,2,3,4,5 and g(x)g(x) has a constant term of 5!5!.

Find g(6)g(6) .


Bonus: Generalize this.

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