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A276639
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Triangle T(m, n) = the number of point-labeled graphs with n points and m edges, no points isolated. By rows, n >= 0, ceiling(n/2) <= m <= binomial(n,2).
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2
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1, 1, 3, 1, 3, 16, 15, 6, 1, 30, 135, 222, 205, 120, 45, 10, 1, 15, 330, 1581, 3760, 5715, 6165, 4945, 2997, 1365, 455, 105, 15, 1, 315, 4410, 23604, 73755, 159390, 259105, 331716, 343161, 290745, 202755, 116175, 54257, 20349, 5985, 1330, 210, 21, 1
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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T(n, m) = Sum_{k=0,..n} binomial(n, k) * (-1)^(n-k) * A084546(k, m).
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EXAMPLE
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Triangle T(n, m) begins:
n/m 0 1 2 3 4 5 6 7 8 9 10
0 1 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 0 0 0 0
3 0 0 3 1 0 0 0 0 0 0 0
4 0 0 3 16 15 6 1 0 0 0 0
5 0 0 0 30 135 222 205 120 45 10 1
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MATHEMATICA
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Table[Sum[Binomial[n, k] (-1)^(n - k) Binomial[Binomial[k, 2], m], {k, 0, n}], {n, 7}, {m, Ceiling[n/2], Binomial[n, 2]}] /. {} -> {1} // Flatten (* Michael De Vlieger, Sep 19 2016 *)
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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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