%I
%S 2,3,27,18209,2369751602470,5960531437867327674538684858601298,
%T 479047836152505670895481842190009123676957243077039687942939196956404642582185242435050
%N Number of labeled T_0hypergraphs with n distinct hyperedges (empty hyperedge excluded).
%C A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.
%F Column sums of A059087.
%F a(n) = Sum_{k = 0..n} (1)^(nk)*A059086(k); a(n) = (1/n!)*Sum_{k = 0..n+1} stirling1(n+1, k)*floor(( 2^(k1))!*exp(1)).
%e a(2)=27; There are 27 labeled T_0hypergraphs with 2 distinct hyperedges (empty hyperedge excluded): 3 2node hypergraphs, 12 3node hypergraphs and 12 4node hypergraphs.
%e a(3) = (1/3!)*(6*[1!*e]+11*[2!*e]6*[4!*e]+[8!*e]) = (1/3!)*(6*2+11*56*65+109601) = 18209, where [k!*e] := floor(k!*exp(1)).
%p with(combinat): Digits := 1000: for n from 0 to 8 do printf(`%d,`,(1/n!)*sum(stirling1(n+1,k)*floor((2^(k1))!*exp(1)), k=0..n+1)) od:
%Y Cf. A059084A059088.
%K easy,nonn
%O 0,1
%A Goran Kilibarda, _Vladeta Jovovic_, Dec 27 2000
%E More terms from _James A. Sellers_, Jan 24 2001
