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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). 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A154912 A133921 A021210

Adjacent sequences:  A285621 A285622 A285623 * A285625 A285626 A285627

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Apr 22 2017

STATUS

approved

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Last modified June 19 05:33 EDT 2019. Contains 324218 sequences. (Running on oeis4.)