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A322706
Regular triangle read by rows where T(n,k) is the number of k-regular k-uniform hypergraphs spanning n vertices.
1
1, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 12, 12, 1, 0, 1, 70, 330, 70, 1, 0, 1, 465, 11205, 11205, 465, 1, 0, 1, 3507, 505505, 2531200, 505505, 3507, 1, 0
OFFSET
1,8
COMMENTS
We define a hypergraph to be any finite set of finite nonempty sets. A hypergraph is k-uniform if all edges contain exactly k vertices, and k-regular if all vertices belong to exactly k edges. The span of a hypergraph is the union of its edges.
EXAMPLE
Triangle begins:
1
1 0
1 1 0
1 3 1 0
1 12 12 1 0
1 70 330 70 1 0
1 465 11205 11205 465 1 0
1 3507 505505 2531200 505505 3507 1 0
Row 4 counts the following hypergraphs:
{{1}{2}{3}{4}} {{12}{13}{24}{34}} {{123}{124}{134}{234}}
{{12}{14}{23}{34}}
{{13}{14}{23}{24}}
MATHEMATICA
Table[Table[SeriesCoefficient[Product[1+Times@@x/@s, {s, Subsets[Range[n], {k}]}], Sequence@@Table[{x[i], 0, k}, {i, n}]], {k, 1, n}], {n, 1, 6}]
CROSSREFS
Row sums are A322705. Second column is A001205. Third column is A110101.
Sequence in context: A034374 A261318 A103879 * A051722 A357354 A166408
KEYWORD
nonn,more,tabl
AUTHOR
Gus Wiseman, Dec 23 2018
STATUS
approved