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I was wondering if anyone knew how to obtain a simpler closed form of the following sum(or had any other insights regarding it): $$\sum_{k=0}^n (-1)^k{n \choose k} C_{2n-2-k} $$ Here $C_n = \frac{1}{n+...

One could imagine defining various notions of higher-dimensional Catalan numbers, by generalizing objects they count. For example, because the Catalan numbers count the triangulations of convex ...