Could we find the n-th term formula for recursive formula $x_{n+1} = {x_n{({x_n \over {x_n+7}}+43)^3}}$

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I have the recursive sequence

$x_0=a$

$x_{n+1} = {x_n{({x_n \over {x_n+7}}+43)^3}}$

could we find the n-th term formula, as we have such for geometric progression.

May be you have any suggestion for good book where such question investigated.