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

0,5

Links

Alois P. Heinz, Rows n = 0..50, flattened

Eric Weisstein's World of Mathematics, Plane partition

Wikipedia, Plane partition

Formula

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

Example

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;

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.

Sequence in context: A159584 A257653 A246834 * A262294 A080779 A355090

Adjacent sequences: A319727 A319728 A319729 * A319731 A319732 A319733

Keyword

nonn,tabl

Author

Alois P. Heinz, Sep 26 2018

Status

approved