This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A059089 #8 Jul 02 2025 16:02:00
%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.
%K A059089 easy,nonn
%O A059089 0,1
%A A059089 Goran Kilibarda, _Vladeta Jovovic_, Dec 27 2000
%E A059089 More terms from _James Sellers_, Jan 24 2001