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Conjectured Somos-like closed form of recurrences with polynomial coefficients

From Our short paper For polynomial $F$ with integer coefficients, define the recurrence $f(n)=F(n,f(n-1),f(n-2),...,f(n-d))$. We conjecture that $f(n)$ satisfy Somos like sequence $f(n)=\frac{G(f(n-1)...
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