Certain diagonal invariants of the iterated polynomial sequence p_n(x) = p_{n-1}(x)^2 - 2 are shown to be weighted Catalan tree sums, equal in closed form to 2(-1)^k/(2k)!.
When is a 2-Power Cyclotomic Extension cyclic?
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This paper characterizes the cyclicity property of $2$-power cyclotomic extensions through various means: the structure of the Galois groups, the nature of their subextensions, tower decompositions, and, most importantly, specific conditions on the base field.
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A study of a recursive sequence of polynomials revealing weighted Catalan Numbers
Certain diagonal invariants of the iterated polynomial sequence p_n(x) = p_{n-1}(x)^2 - 2 are shown to be weighted Catalan tree sums, equal in closed form to 2(-1)^k/(2k)!.