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 A285529 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. 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA 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 EXAMPLE 1, 2,   2, 6,   12,   6, 32,  96,   96,   32, 320, 1280, 1920, 1280, 320, ... MATHEMATICA 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 CROSSREFS Row sums give A095340. Columns for k=0-3: A123903, A095338, A038094, A038096. Sequence in context: A241669 A178802 A156992 * A305215 A219694 A054481 Adjacent sequences:  A285526 A285527 A285528 * A285530 A285531 A285532 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Apr 20 2017 STATUS approved

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Last modified June 20 09:51 EDT 2021. Contains 345162 sequences. (Running on oeis4.)