A285624 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).

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

Offset

1,3

Links

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

Formula

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).

Example

1, 1;
4, 8, 4;
24, 96, 144, 96, 24;
512, 4096, 14336, 28672, 35840, 28672, 14336, 4096, 512;
  ...

Mathematica

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]]]

Crossrefs

Sequence in context: A255293 A019246 A019192 * A356636 A334957 A154912

Adjacent sequences: A285621 A285622 A285623 * A285625 A285626 A285627

Keyword

nonn,tabf

Author

Geoffrey Critzer, Apr 22 2017

Status

approved