A259049 Number of self-complementary plane partitions in a (2n)-cube.

1, 4, 400, 960400, 54218191104, 71410553858811024, 2186315392560559723530496, 1552832545847343203950118294425600, 25554649541466337940020968722797075170918400, 9736551559782513812975251884508283964266367033264640000

Offset: 0

Author

Peter J. Taylor, Jun 17 2015

Keywords

• nonn
• easy

Comments

Odd cubes have no self-complementary plane partitions.

Links

• R. P. Stanley, Symmetries of Plane Partitions, J. Comb. Theory Ser. A 43 (1986), 103-113.
• P. J. Taylor, Counting distinct dimer hex tilings, Preprint, 2015.

Crossrefs

Cf. A008793.

Programs

PARI

a(n) = prod(i=0, n-1, i!^2*(i+2*n)!^2 / (i+n)!^4) \\ Michel Marcus, Jun 18 2015

Formula

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

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