A383354 Squares of plane partition numbers.

1, 1, 9, 36, 169, 576, 2304, 7396, 25600, 79524, 250000, 737881, 2187441, 6175225, 17363889, 47320641, 127622209, 336135556, 876219201, 2240128900, 5666777284, 14112014436, 34772925625, 84554753089, 203576025636, 484461937089, 1142215875025, 2665572144964, 6166451098756

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Eric Weisstein's World of Mathematics, Plane Partition

Formula

a(n) = [(x*y)^n] Product_{k>=1} 1 / ((1 - x^k) * (1 - y^k))^k.

a(n) = A000219(n)^2.

Mathematica

nmax = 28; CoefficientList[Series[Product[1/(1 - x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x]^2

Crossrefs

Cf. A000219, A001255, A304990.

Sequence in context: A245416 A265837 A383072 * A264359 A280353 A110752

Adjacent sequences: A383351 A383352 A383353 * A383355 A383356 A383357

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 24 2025

Status

approved