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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
OFFSET
0,5
LINKS
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.
Sequence in context: A159584 A257653 A246834 * A262294 A080779 A355090
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 26 2018
STATUS
approved