%I A059089
%S A059089 2,3,27,18209,2369751602470,5960531437867327674538684858601298,
%T A059089 479047836152505670895481842190009123676957243077039687942939196956404642582185242435050
%N A059089 Number of labeled T_0-hypergraphs with n distinct hyperedges (empty hyperedge 
               excluded).
%C A059089 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 A059089 Column sums of A059087.
%F A059089 a(n) = Sum_{k = 0..n} (-1)^(n-k)*A059086(k); a(n) = (1/n!)*Sum_{k = 0..n+1} 
               stirling1(n+1, k)*floor(( 2^(k-1))!*exp(1)).
%e A059089 a(2)=27; There are 27 labeled T_0-hypergraphs with 2 distinct hyperedges 
               (empty hyperedge excluded): 3 2-node hypergraphs, 12 3-node hypergraphs 
               and 12 4-node hypergraphs.
%e A059089 a(3) = (1/3!)*(-6*[1!*e]+11*[2!*e]-6*[4!*e]+[8!*e]) = (1/3!)*(-6*2+11*5-6*65+109601) 
               = 18209, where [k!*e] := floor(k!*exp(1)).
%p A059089 with(combinat): Digits := 1000: for n from 0 to 8 do printf(`%d,`,(1/
               n!)*sum(stirling1(n+1,k)*floor((2^(k-1))!*exp(1)), k=0..n+1)) od:
%Y A059089 Cf. A059084-A059088.
%Y A059089 Sequence in context: A126203 A126655 A132533 this_sequence A098812 A037320 
               A010344
%Y A059089 Adjacent sequences: A059086 A059087 A059088 this_sequence A059090 A059091 
               A059092
%K A059089 easy,nonn
%O A059089 0,1
%A A059089 Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2000
%E A059089 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 24 2001