Same old, same old

Algebra Level 3

f(1)=4,f(2)=9,f(3)=20,f(4)=44,f(5)=88 \large f(1) = 4, f(2) = 9, f(3) = 20, f(4) = 44, f(5) = 88

Let f(x)f(x) be a 5th degree monic polynomial such that it satisfies the equations above. Find the value of f(6)f(6).

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