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%I #11 Apr 26 2017 16:12:40
%S 1,1,4,8,4,24,96,144,96,24,512,4096,14336,28672,35840,28672,14336,
%T 4096,512,163840,2621440,19660800,91750400,298188800,715653120,
%U 1312030720,1874329600,2108620800,1874329600,1312030720,715653120,298188800,91750400,19660800,2621440,163840
%N Triangle read by rows: T(n,k) is the number of vertices with degree k counted over all hypergraphs on n labeled nodes, n>=1,0<=k<=2^(n-1).
%F E.g.f. for column k: x * Sum_{n>=0} binomial(2^n,k)*2^(2^n-1)*x^n/n!.
%F T(n,k) = n * binomial(2^(n-1),k) * 2^(2^(n-1)-1).
%e 1, 1;
%e 4, 8, 4;
%e 24, 96, 144, 96, 24;
%e 512, 4096, 14336, 28672, 35840, 28672, 14336, 4096, 512;
%e ...
%t nn = 5; Grid[ Map[Select[#, # > 0 &] &,
%t Drop[Transpose[Table[A[z_] :=Sum[Binomial[2^n, k] 2^(2^n - 1) z^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[ z A[z], {z, 0, nn}], z], {k, 0, 2^(nn - 1)}]], 1]]]
%K nonn,tabf
%O 1,3
%A _Geoffrey Critzer_, Apr 22 2017
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