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Number of lattice paths in the lattice [0..2n] X [0..2n] X [0..2n] which do not pass through the point (n,n,n). Number of paths through a lattice containing a "hole".
2

%I #9 Feb 16 2016 10:04:53

%S 54,26550,14330736,8264889270,4978317147804,3090501687886704,

%T 1961313438507566400,1265749551338006549430,827693426702217868006500,

%U 547017649101008848332870300,364691794467483796757326646400,244920478151771001164678945670000

%N Number of lattice paths in the lattice [0..2n] X [0..2n] X [0..2n] which do not pass through the point (n,n,n). Number of paths through a lattice containing a "hole".

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LatticePath.html">Lattice Path.</a>

%F a(n) = s(3,2n)-s(3,n)^2.

%t Table[Factorial[6n]/Factorial[2n]^3-(Factorial[3n]/Factorial[n]^3)^2, {n, 1, 10}]

%Y Cf. A006480, A071801, A071803.

%K easy,nice,nonn

%O 1,1

%A _T. D. Noe_, Jun 06 2002