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A319600 Number T(n,k) of plane partitions of n into parts of exactly k sorts; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 5
1, 0, 1, 0, 3, 4, 0, 6, 22, 18, 0, 13, 96, 198, 120, 0, 24, 330, 1272, 1800, 840, 0, 48, 1146, 7518, 19152, 20640, 7920, 0, 86, 3518, 36684, 148200, 274080, 234720, 75600, 0, 160, 10946, 177438, 1080960, 3083640, 4462560, 3180240, 887040, 0, 282, 32102, 788928, 6952440, 28621920, 62056080, 73175760, 44432640, 10886400 (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) = Sum_{i=0..k} (-1)^i * C(k,i) * A306100(n,k-i).

T(n,k) = k! * A319730(n,k).

EXAMPLE

Triangle T(n,k) begins:

  1;

  0,   1;

  0,   3,     4;

  0,   6,    22,     18;

  0,  13,    96,    198,     120;

  0,  24,   330,   1272,    1800,     840;

  0,  48,  1146,   7518,   19152,   20640,    7920;

  0,  86,  3518,  36684,  148200,  274080,  234720,   75600;

  0, 160, 10946, 177438, 1080960, 3083640, 4462560, 3180240, 887040;

CROSSREFS

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

Row sums give A319601.

Main diagonal gives A053529.

Cf. A255970, A319730.

Sequence in context: A105826 A110665 A063441 * A092894 A276563 A011338

Adjacent sequences:  A319597 A319598 A319599 * A319601 A319602 A319603

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 24 2018

STATUS

approved

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Last modified November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)