Consider the recursion $x_n = 3(x_0x_{n−1} + x_1x_{n−2} + · · · + x_{n−1}x_0)$, with $x_0 = 1$. Find closed form for $x_n$.
Since this is non linear, I cannot assume $x_n=\lambda^{n}$ and try to solve it using a quadratic equation. Is there any tricks I can cancel out terms to find the closed form?
P.S. I did some research and for nonlinear recursion there is no specific rigorous formula I can follow to solve for the closed form so I am wondering if there is a trick in this question.