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A084546
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Triangle read by rows: T(n,k) = C( C(n,2), k) for n >= 0, 0 <= k <= C(n,2).
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19
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1, 1, 1, 1, 1, 3, 3, 1, 1, 6, 15, 20, 15, 6, 1, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1, 1, 21, 210, 1330, 5985, 20349, 54264, 116280, 203490, 293930, 352716, 352716, 293930, 203490, 116280, 54264, 20349, 5985, 1330, 210, 21, 1
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OFFSET
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0,6
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COMMENTS
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T(n,k) gives number of labeled simple graphs with n nodes and k edges.
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REFERENCES
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J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 517.
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LINKS
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EXAMPLE
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Triangle begins:
1;
1;
1, 1;
1, 3, 3, 1;
1, 6, 15, 20, 15, 6, 1;
...
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MAPLE
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C:= binomial:
T:= (n, k)-> C( C(n, 2), k):
seq(seq(T(n, k), k=0..C(n, 2)), n=0..10); # Alois P. Heinz, Feb 17 2023
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MATHEMATICA
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Table[Table[Binomial[Binomial[n, 2], k], {k, 0, Binomial[n, 2]}], {n, 1, 7}]//Grid (* Geoffrey Critzer, Apr 28 2011 *)
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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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EXTENSIONS
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STATUS
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approved
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