OFFSET
0,4
COMMENTS
A hypergraph is uniform if all edges have the same size.
Let T be the regular triangle A299354, where column k is the logarithmic transform of the inverse binomial transform of c(d) = 2^binomial(d,k). Then a(n) is the sum of row n.
LINKS
Wikipedia, Hypergraph
EXAMPLE
The a(3) = 5 hypergraphs:
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,3},{2,3}}
MATHEMATICA
nn=10; Table[Sum[SeriesCoefficient[Log[Sum[x^m/m!*(-1)^(m-d)*Binomial[m, d]*2^Binomial[d, k], {m, 0, n}, {d, 0, m}]], {x, 0, n}]*n!, {k, n}], {n, nn}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 18 2018
STATUS
approved