Unknown Catalan Number series!

Algebra Level 4

Let \(F(x) \) be a quartic polynomial that satisfy the \(F(n) =C_ n\), for \(n=1,2,3,4,5\), where \(C_n =\dfrac{(2n)!}{n! (n+1)!}\) denote the \(n^\text{th} \) Catalan number. Find \(F(6) + F(7) \).

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