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A285624
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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).
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0
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1, 1, 4, 8, 4, 24, 96, 144, 96, 24, 512, 4096, 14336, 28672, 35840, 28672, 14336, 4096, 512, 163840, 2621440, 19660800, 91750400, 298188800, 715653120, 1312030720, 1874329600, 2108620800, 1874329600, 1312030720, 715653120, 298188800, 91750400, 19660800, 2621440, 163840
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OFFSET
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1,3
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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(2^n,k)*2^(2^n-1)*x^n/n!.
T(n,k) = n * binomial(2^(n-1),k) * 2^(2^(n-1)-1).
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EXAMPLE
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1, 1;
4, 8, 4;
24, 96, 144, 96, 24;
512, 4096, 14336, 28672, 35840, 28672, 14336, 4096, 512;
...
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MATHEMATICA
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nn = 5; Grid[ Map[Select[#, # > 0 &] &,
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]]]
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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