A variant of Touchard's Catalan number identity
Abstract
It is well known that the Catalan number Cn counts dissections of a regular (n+2)-gon into triangles. Here we count such dissections by number of triangles that contain two sides of the polygon among their three edges, leading to a combinatorial interpretation of the identity Cn =sum1<=k<=n/2 2n-2k n-choose-2k Ck (k(n+2))/(n(n-1)), and illustrating its connection with Touchard's identity.
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