A394283 Number of rectangular plane partitions of n with exactly 2 rows and with rows and columns strictly decreasing.

0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 15, 20, 25, 32, 40, 51, 63, 79, 98, 121, 149, 184, 224, 274, 334, 405, 490, 593, 713, 858, 1029, 1231, 1470, 1754, 2084, 2476, 2935, 3473, 4101, 4839, 5695, 6698, 7862, 9216, 10787, 12614, 14721, 17167, 19989, 23249, 27004, 31337, 36313

Offset

0,6

Links

Table of n, a(n) for n=0..55.

Formula

G.f.: Sum_{k>=1} q^(k*(k+2)) * Product_{i=1..2} Product_{j=1..k} 1/(1 - q^(i+j-1)).

Example

The a(10) = 7 matrices:
  [9] [8] [7] [6] [5 2] [4 2] [4 3]
  [1] [2] [3] [4] [2 1] [3 1] [2 1]

Prog

(PARI) my(N=60, q='q+O('q^N)); concat([0, 0, 0], Vec(sum(k=1, N, q^(k*(k+2))*prod(i=1, 2, prod(j=1, k, 1/(1-q^(i+j-1)))))))

Crossrefs

Column k=2 of A394187.

Cf. A323430, A395924.

Sequence in context: A318053 A061287 A225500 * A064651 A094991 A255575

Adjacent sequences: A394280 A394281 A394282 * A394284 A394285 A394286

Keyword

nonn

Author

Seiichi Manyama, May 10 2026

Status

approved