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a(n) is the number of unordered triples of shortest nonintersecting grid paths joining two opposite corners of an n X n X n grid.
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%I #32 Apr 13 2023 00:28:22

%S 2,1440,5039744,30456915312,244247250106272,2330237215901633376,

%T 25005390829898900970720,292102859220245236374450192,

%U 3638369778575244135648725730848,47651985114895805442163075548018912,649794504408024777960179124905242154688

%N a(n) is the number of unordered triples of shortest nonintersecting grid paths joining two opposite corners of an n X n X n grid.

%C An n X n X n grid is a cube with (n+1)^3 grid points. Each of the three paths has 3*n steps and they intersect only at the start and at the end. Initially, each path will start by moving along distinct coordinate axes.

%Y The two-dimensional version of this sequence is A000891(n-1).

%K nonn

%O 1,1

%A _Janaka Rodrigo_, Apr 11 2023

%E a(4)-a(11) from _Andrew Howroyd_, Apr 11 2023