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A285529
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Triangle read by rows: T(n,k) is the number of nodes of degree k counted over all simple labeled graphs on n nodes, n>=1, 0<=k<=n-1.
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0
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1, 2, 2, 6, 12, 6, 32, 96, 96, 32, 320, 1280, 1920, 1280, 320, 6144, 30720, 61440, 61440, 30720, 6144, 229376, 1376256, 3440640, 4587520, 3440640, 1376256, 229376, 16777216, 117440512, 352321536, 587202560, 587202560, 352321536, 117440512, 16777216
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OFFSET
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1,2
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LINKS
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FORMULA
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E.g.f. for column k: x * Sum_{n>=0} binomial(n,k)*2^binomial(n,2)*x^n/n!.
Sum_{k=1..n-1} T(n,k)*k/2 = A095351(n).
T(n,k) = n*binomial(n-1,k)*2^binomial(n-1,2). - Alois P. Heinz, Apr 21 2017
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EXAMPLE
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1,
2, 2,
6, 12, 6,
32, 96, 96, 32,
320, 1280, 1920, 1280, 320,
...
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MATHEMATICA
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nn = 9; Map[Select[#, # > 0 &] &,
Drop[Transpose[Table[A[z_] := Sum[Binomial[n, k] 2^Binomial[n, 2] z^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[z A[z], {z, 0, nn}], z], {k, 0, nn - 1}]], 1]] // Grid
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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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