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Recent references on the matter at hand include, a lecture slide The Konvalinka-Amdeberhan conjecture and plethystic inverses and a preprint on Counting tanglegrams with species by I. Gessel; the ...

While working on some computations on Hilbert schemes, I came across the following combinatorial problem. Let $D(k,n)$ be the weighted number of binary trees (children are left/right) with $n$ ...