|
%I #14 Apr 21 2017 08:30:02
%S 1,2,2,6,12,6,32,96,96,32,320,1280,1920,1280,320,6144,30720,61440,
%T 61440,30720,6144,229376,1376256,3440640,4587520,3440640,1376256,
%U 229376,16777216,117440512,352321536,587202560,587202560,352321536,117440512,16777216
%N 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.
%F E.g.f. for column k: x * Sum_{n>=0} binomial(n,k)*2^binomial(n,2)*x^n/n!.
%F Sum_{k=1..n-1} T(n,k)*k/2 = A095351(n).
%F T(n,k) = n*binomial(n-1,k)*2^binomial(n-1,2). - _Alois P. Heinz_, Apr 21 2017
%e 1,
%e 2, 2,
%e 6, 12, 6,
%e 32, 96, 96, 32,
%e 320, 1280, 1920, 1280, 320,
%e ...
%t nn = 9; Map[Select[#, # > 0 &] &,
%t 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
%Y Row sums give A095340.
%Y Columns for k=0-3: A123903, A095338, A038094, A038096.
%K nonn,tabl
%O 1,2
%A _Geoffrey Critzer_, Apr 20 2017
|
