Pattern avoidance is not P-recursive

Let $F \subset S_k$ be a finite set of permutations and let $C_n(F)$ denote the number of permutations $\sigma$ in $S_n$ avoiding the set of patterns $F$. The Noonan-Zeilberger conjecture states that the sequence ${C_n(F)}$ is P-recursive. We use Computability Theory to disprove this conjecture.

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