Elizalde–Noy conjecture for the pattern 1423

Let $P_{1423}(0,z)$ be the generating function for permutations avoiding the consecutive pattern $1423$, and write

$$\omega_{1423}(0,z)=\frac{1}{P_{1423}(0,z)}.$$

A formal power series is D-finite if it satisfies a linear differential equation with polynomial coefficients. Elizalde and Noy's conjecture. The generating function $\omega_{1423}(0,z)$ is not D-finite. This is the specific counterexample suggested in their broader conjecture about reciprocal generating functions for consecutive patterns.