$\left\{\begin{matrix}b=\frac{\left(n-1\right)!\left(n+3\right)!-n!\left(n+1\right)!}{66\left(n-1\right)!\left(n+1\right)!}\text{, }&\left(n-1\right)!\left(n+1\right)!\neq 0\text{ and }\left(n+1\right)!\neq 0\text{ and }\left(n-1\right)!\neq 0\\b\in \mathrm{R}\text{, }&\left(n-1\right)!\left(n+3\right)!-n!\left(n+1\right)!=0\text{ and }\left(n-1\right)!\left(n+1\right)!=0\text{ and }\left(n+1\right)!\neq 0\text{ and }\left(n-1\right)!\neq 0\end{matrix}\right.$