\[c\cdot a_na_{n-1} + c_1\cdot a_n + c_2\cdot a_{n-1} + c_3=0 \]
where, $c_1, c_2, c_3$ and $c$ are constants, $c\neq 0$, and $a_0\neq-\frac{c_1}{c}$ is given.
Does a general solution in CLOSED FORM to this non-linear recurrence exist ?
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*Note: This is an open question. Most non-linear recurrences don't have a solution in closed form. But, I can't seem to find any resource with a treatment of this type of recurrence. Any link/resource/reference/discussion would be helpful...
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