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A319600
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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.
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5
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n,k) = Sum_{i=0..k} (-1)^i * C(k,i) * A306100(n,k-i).
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EXAMPLE
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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;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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