%I #16 Jul 15 2018 13:21:33
%S 1,1,1,5,50,1713,1101990,68715891672,1180735735356264714926,
%T 170141183460507906731293351306487161569,
%U 7237005577335553223087828975127304177495735363998991435497132228228565768846
%N Number of labeled connected uniform hypergraphs spanning n vertices.
%C A hypergraph is uniform if all edges have the same size.
%C 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.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hypergraph">Hypergraph</a>
%e The a(3) = 5 hypergraphs:
%e {{1,2,3}}
%e {{1,2},{1,3}}
%e {{1,2},{2,3}}
%e {{1,3},{2,3}}
%e {{1,2},{1,3},{2,3}}
%t 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}]
%Y Cf. A000005, A001315, A006126, A006129, A038041, A048143, A298422, A299354, A299471, A306020, A306021.
%K nonn
%O 0,4
%A _Gus Wiseman_, Jun 18 2018