Conjectured generating function for permutations containing four occurrences of 321

Let $s_n((3,2,1),r)$ denote the number of permutations of length $n$ containing exactly $r$ occurrences of the pattern $(3,2,1)$, and let

$$F_{(3,2,1),r}(x)=\sum_{n\geq 0}s_n((3,2,1),r)x^n.$$

The 321 four-occurrence generating-function conjecture.

$$F_{(3,2,1),4}(x)=\frac{-1}{2x^9}\left[(-1+12x-50x^2+65x^3+107x^4-437x^5+588x^6-492x^7+314x^8-108x^9+3x^{10})+\sqrt{1-4x}(-1+10x-32x^2+17x^3+107x^4-245x^5+256x^6-192x^7+102x^8-18x^9-x^{10})\right].$$

This is one of the explicitly conjectured algebraic generating functions for the number of occurrences of the decreasing pattern of length three. The supplied text gives no resolution status for this formula.