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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
OFFSET
0,5
LINKS
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.
Sequence in context: A105826 A110665 A063441 * A092894 A276563 A011338
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 24 2018
STATUS
approved