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A360625
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Triangle read by rows: T(n,k) is the k-th Lie-Betti number of a complete graph on n vertices, n >= 1, k >= 0.
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7
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1, 1, 1, 2, 2, 1, 1, 3, 8, 12, 8, 3, 1, 1, 4, 20, 56, 84, 90, 84, 56, 20, 4, 1, 1, 5, 40, 176, 440, 835, 1423, 1980, 1980, 1423, 835, 440, 176, 40, 5, 1, 1, 6, 70, 441, 1616, 4600, 11984, 26824, 46800, 63254, 70784, 70784, 63254, 46800, 26824, 11984, 4600, 1616, 441, 70, 6, 1
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OFFSET
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1,4
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LINKS
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EXAMPLE
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Triangle begins:
k= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
n=1: 1 1
n=2: 1 2 2 1
n=3: 1 3 8 12 8 3 1
n=4: 1 4 20 56 84 90 84 56 20 4 1
n=5: 1 5 40 176 440 835 1423 1980 1980 1423 835 440 176 40 5 1
...
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PROG
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(SageMath) # uses[betti_numbers, LieAlgebraFromGraph from A360571]
if n == 1: return [1, 1]
return betti_numbers(LieAlgebraFromGraph(graphs.CompleteGraph(n)))
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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