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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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
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 A319830

Adjacent sequences:  A319727 A319728 A319729 * A319731 A319732 A319733

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 26 2018

STATUS

approved

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Last modified January 21 22:47 EST 2020. Contains 331129 sequences. (Running on oeis4.)