%I A059086
%S A059086 2,5,30,18236,2369751620679,5960531437867327674541054610203768,
%T A059086 479047836152505670895481842190009123676957243077039693903470634823732317120870101036348
%N A059086 Number of labeled T_0-hypergraphs with n distinct hyperedges (empty hyperedge 
               included).
%C A059086 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 A059086 a(n) = (1/n!)*Sum_{k = 0..n} stirling1(n, k)*floor((2^k)!*exp(1)).
%e A059086 a(2)=30; There are 30 labeled T_0-hypergraphs with 2 distinct hyperedges 
               (empty hyperedge included): 1 1-node hypergraph, 5 2-node hypergraphs, 
               12 3-node hypergraphs and 12 4-node hypergraphs.
%e A059086 a(3) = (1/3!)*(2*[2!*e]-3*[4!*e]+[8!*e]) = (1/3!)*(2*5-3*65+109601) = 
               18236, where [k!*e] := floor (k!*exp(1)).
%p A059086 with(combinat): Digits := 1000: for n from 0 to 8 do printf(`%d,`,(1/
               n!)*sum(stirling1(n, k)*floor((2^k)!*exp(1)), k=0..n)) od:
%Y A059086 Column sums of A059084.
%Y A059086 Cf. A059084, A059085, A059087-A059089.
%Y A059086 Sequence in context: A129951 A127298 A000133 this_sequence A107389 A077483 
               A119242
%Y A059086 Adjacent sequences: A059083 A059084 A059085 this_sequence A059087 A059088 
               A059089
%K A059086 easy,nonn
%O A059086 0,1
%A A059086 Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2000
%E A059086 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 24 2001