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Number of self-complementary plane partitions in a (2n)-cube.
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%I #12 Feb 13 2016 17:40:02

%S 1,4,400,960400,54218191104,71410553858811024,

%T 2186315392560559723530496,1552832545847343203950118294425600,

%U 25554649541466337940020968722797075170918400,9736551559782513812975251884508283964266367033264640000

%N Number of self-complementary plane partitions in a (2n)-cube.

%C Odd cubes have no self-complementary plane partitions.

%H R. P. Stanley, <a href="http://dx.doi.org/10.1016/0097-3165(86)90028-2">Symmetries of Plane Partitions</a>, J. Comb. Theory Ser. A 43 (1986), 103-113.

%H P. J. Taylor, <a href="http://cheddarmonk.org/papers/distinct-dimer-hex-tilings.pdf">Counting distinct dimer hex tilings</a>, Preprint, 2015.

%F a(n) = Product_{i=0..n-1} i!^2 (i+2n)!^2 / (i+n)!^4.

%F a(n) = A008793(n)^2.

%o (PARI) a(n) = prod(i=0, n-1, i!^2*(i+2*n)!^2 / (i+n)!^4) \\ _Michel Marcus_, Jun 18 2015

%Y Cf. A008793.

%K nonn,easy

%O 0,2

%A _Peter J. Taylor_, Jun 17 2015