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 A322705 Number of k-uniform k-regular hypergraphs spanning n vertices, for some 1 <= k <= n. 2
 1, 1, 1, 2, 5, 26, 472, 23342 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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. LINKS EXAMPLE The a(3) = 2 hypergraphs:   {{1},{2},{3}}   {{1,2},{1,3},{2,3}} The a(4) = 5 hypergraphs:   {{1},{2},{3},{4}}   {{1,2},{1,3},{2,4},{3,4}}   {{1,2},{1,4},{2,3},{3,4}}   {{1,3},{1,4},{2,3},{2,4}}   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}} The a(5) = 26 hypergraphs:   {{1},{2},{3},{4},{5}}   {{1,2},{1,3},{2,4},{3,5},{4,5}}   {{1,2},{1,3},{2,5},{3,4},{4,5}}   {{1,2},{1,4},{2,3},{3,5},{4,5}}   {{1,2},{1,4},{2,5},{3,4},{3,5}}   {{1,2},{1,5},{2,3},{3,4},{4,5}}   {{1,2},{1,5},{2,4},{3,4},{3,5}}   {{1,3},{1,4},{2,3},{2,5},{4,5}}   {{1,3},{1,4},{2,4},{2,5},{3,5}}   {{1,3},{1,5},{2,3},{2,4},{4,5}}   {{1,3},{1,5},{2,4},{2,5},{3,4}}   {{1,4},{1,5},{2,3},{2,4},{3,5}}   {{1,4},{1,5},{2,3},{2,5},{3,4}}   {{1,2,3},{1,2,4},{1,3,5},{2,4,5},{3,4,5}}   {{1,2,3},{1,2,4},{1,4,5},{2,3,5},{3,4,5}}   {{1,2,3},{1,2,5},{1,3,4},{2,4,5},{3,4,5}}   {{1,2,3},{1,2,5},{1,4,5},{2,3,4},{3,4,5}}   {{1,2,3},{1,3,4},{1,4,5},{2,3,5},{2,4,5}}   {{1,2,3},{1,3,5},{1,4,5},{2,3,4},{2,4,5}}   {{1,2,4},{1,2,5},{1,3,4},{2,3,5},{3,4,5}}   {{1,2,4},{1,2,5},{1,3,5},{2,3,4},{3,4,5}}   {{1,2,4},{1,3,4},{1,3,5},{2,3,5},{2,4,5}}   {{1,2,4},{1,3,5},{1,4,5},{2,3,4},{2,3,5}}   {{1,2,5},{1,3,4},{1,3,5},{2,3,4},{2,4,5}}   {{1,2,5},{1,3,4},{1,4,5},{2,3,4},{2,3,5}}   {{1,2,3,4},{1,2,3,5},{1,2,4,5},{1,3,4,5},{2,3,4,5}} MATHEMATICA Table[Sum[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 of A322706. Cf. A005176, A058891, A059441, A116539, A295193, A299353, A306021, A319056, A319189, A319190, A319612, A321721, A322704. Sequence in context: A111195 A323293 A258868 * A167007 A064006 A003095 Adjacent sequences:  A322702 A322703 A322704 * A322706 A322707 A322708 KEYWORD nonn,more AUTHOR Gus Wiseman, Dec 23 2018 STATUS approved

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Last modified March 29 20:20 EDT 2020. Contains 333117 sequences. (Running on oeis4.)