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 A059088 #12 Jul 02 2025 16:02:00
%S A059088 1,2,6,108,32076,2147160096,9223372004645279520,
%T A059088 170141183460469231537996491317719562880,
%U A059088 57896044618658097711785492504343953921871039195927143534211473291570199939840
%N A059088 Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge excluded).
%C A059088 A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.
%H A059088 <a href="/A059087/a059087.pdf">Illustration of initial terms of A059087, A059088</a>
%F A059088 Row sums of A059087.
%F A059088 a(n) = A059085(n)/2.
%F A059088 a(n) = Sum_{k=0..n} stirling1(n, k)*2^((2^k)-1).
%e A059088 There are 108 labeled 3-node T_0-hypergraphs without multiple hyperedges (empty hyperedge excluded): 12 with 2 hyperedges, 32 with 3 hyperedges,35 with 4 hyperedges, 21 with 5 hyperedges, 7 with 6 hyperedges and 1 with 7 hyperedges.
%p A059088 with(combinat): for n from 0 to 15 do printf(`%d,`,(1/2)*sum(stirling1(n,k)*2^(2^k), k= 0..n)) od:
%t A059088 Table[Sum[StirlingS1[n, k]*2^((2^k)-1), {k,0,n}], {n,0,10}] (* _G. C. Greubel_, Oct 06 2017 *)
%Y A059088 Cf. A059084-A059087, A059089.
%K A059088 easy,nonn
%O A059088 0,2
%A A059088 Goran Kilibarda, _Vladeta Jovovic_, Dec 27 2000
%E A059088 More terms from _James Sellers_, Jan 24 2001