A319730 Number T(n,k) of plane partitions of n into parts of exactly k sorts which are introduced in ascending order; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

1, 0, 1, 0, 3, 2, 0, 6, 11, 3, 0, 13, 48, 33, 5, 0, 24, 165, 212, 75, 7, 0, 48, 573, 1253, 798, 172, 11, 0, 86, 1759, 6114, 6175, 2284, 326, 15, 0, 160, 5473, 29573, 45040, 25697, 6198, 631, 22, 0, 282, 16051, 131488, 289685, 238516, 86189, 14519, 1102, 30

Offset: 0

Author

Alois P. Heinz, Sep 26 2018

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) begins:
  1;
  0,   1;
  0,   3,     2;
  0,   6,    11,      3;
  0,  13,    48,     33,      5;
  0,  24,   165,    212,     75,      7;
  0,  48,   573,   1253,    798,    172,    11;
  0,  86,  1759,   6114,   6175,   2284,   326,    15;
  0, 160,  5473,  29573,  45040,  25697,  6198,   631,   22;
  0, 282, 16051, 131488, 289685, 238516, 86189, 14519, 1102, 30;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..50, flattened
• Eric Weisstein's World of Mathematics, Plane partition
• Wikipedia, Plane partition

Crossrefs

Columns k=0-1 give: A000007, A000219 (for n>0).

Main diagonal gives A000041.

Row sums give A319731.

T(2n,n) gives A319732.

Cf. A256130, A319600.

Formula

T(n,k) = 1/k! * A319600(n,k).