A362207 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.

2, 1440, 5039744, 30456915312, 244247250106272, 2330237215901633376, 25005390829898900970720, 292102859220245236374450192, 3638369778575244135648725730848, 47651985114895805442163075548018912, 649794504408024777960179124905242154688

Offset: 1

Author

Janaka Rodrigo, Apr 11 2023

Keywords

• nonn

Comments

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.

Crossrefs

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

Extensions

a(4)-a(11) from Andrew Howroyd, Apr 11 2023