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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

Table of n, a(n) for n=1..36.

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.)