Generalized Catalan numbers C(3,n), where the (m,n)-th Catalan is the number of paths in R^m from the origin to the point (n,...,n,(m-1)n) with m kinds of moves such that the path never rises above the hyperplane x_m = x_1+...+x_{m-1}.

A270577

Generalized Catalan numbers C(3,n), where the (m,n)-th Catalan is the number of paths in R^m from the origin to the point (n,...,n,(m-1)n) with m kinds of moves such that the path never rises above the hyperplane x_m = x_1+...+x_{m-1}.