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I have already known QPermutationDerangement: It describes the distribution $$ d_n(q)=\sum_{\sigma \in D_n} q^{\operatorname{maj}(\sigma)} $$ Where we sum over all derangements of an $n$ element set. ...

Let $C_n=\frac1{n+1}\binom{2n}n$ be the all-familiar Catalan numbers. Then, the following identity has received enough attention in the literature (for example, Lagrange Inversion: When and How): \...

Let $C_n=\frac1{n+1}\binom{2n}n$ denote the Catalan numbers. This question is motivated by the (unanswered) MO post by Alexander Burstein and my own (answered by Fedor Petrov) MO post. Specifically, ...