Let $$A_{n}=\sum_{i=0}^{n-3}(-1)^{n+i-2}\dfrac{13n^2-31n-10ni+9i+i^2+16}{(3n-i-3)(3n-i-4)(2n-i-3)!\cdot i!}$$

I want find the $A_{n}$ recursive relations,such as following form $$A_{n}=B_{n}+C_{n}A_{n-1}+D_{n}A_{n-2}+\cdots$$ I have try sometimes,and can't find it,can you help me?

This question has been asked on MSE here without receiving any answers.

Let $$A_{n}=\sum_{i=0}^{n-3}(-1)^{n+i-2}\dfrac{13n^2-31n-10ni+9i+i^2+16}{(3n-i-3)(3n-i-4)(2n-i-3)!\cdot i!}$$

I want find the $A_{n}$ recursive relations,such as following form $$A_{n}=B_{n}+C_{n}A_{n-1}+D_{n}A_{n-2}+\cdots$$ I have try sometimes,and can't find it,can you help me?

This question has been asked on MSE here without receiving any answers.