A320606 Regular triangle read by rows where T(n,k) is the number of k-uniform hypergraphs spanning n labeled vertices where every two vertices appear together in some edge, n >= 0, 0 <= k <= n.

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 5, 1, 0, 0, 1, 388, 16, 1, 0, 0, 1, 477965, 27626, 42, 1

Offset

1,14

Links

Table of n, a(n) for n=1..28.

Example

Triangle begins:
      1
      0      1
      0      0      1
      0      0      1      1
      0      0      1      5      1
      0      0      1    388     16      1
      0      0      1 477965  27626     42      1

Mathematica

Table[Length[Select[Subsets[If[k==0, {}, Subsets[Range[n], {k}]]], And[Union@@#==Range[n], Length[Union@@(Subsets[#, {2}]&/@#)]==Binomial[n, 2]]&]], {n, 0, 6}, {k, 0, n}]

Crossrefs

Row sums are A321134. Column k = 3 is A302394 without the initial terms.

Cf. A058891, A116539, A301922, A306021, A319189, A320444.

Sequence in context: A180977 A371761 A269129 * A343016 A058177 A345373

Adjacent sequences: A320603 A320604 A320605 * A320607 A320608 A320609

Keyword

nonn,tabl,more

Author

Gus Wiseman, Jan 10 2019

Status

approved