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 A059085 #12 Jul 02 2025 16:02:00
%S A059085 2,4,12,216,64152,4294320192,18446744009290559040,
%T A059085 340282366920938463075992982635439125760,
%U A059085 115792089237316195423570985008687907843742078391854287068422946583140399879680
%N A059085 Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge included).
%C A059085 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 A059085 V. Jovovic, <a href="/A059084/a059084.pdf">Illustration of initial terms of A059084, A059085</a>
%F A059085 Row sums of A059084.
%F A059085 a(n) = Sum_{k=0..n} stirling1(n, k)*2^(2^k).
%F A059085 E.g.f.: Sum(2^(2^n)*log(1+x)^n/n!, n=0..infinity) = Sum(log(2)^n*(1+x)^(2^n)/n!, n=0..infinity). - _Vladeta Jovovic_, May 10 2004
%e A059085 There are 216 labeled 3-node T_0-hypergraphs without multiple hyperedges (empty hyperedge included): 12 with 2 hyperedges, 44 with 3 hyperedges,67 with 4 hyperedges, 56 with 5 hyperedges, 28 with 6 hyperedges, 8 with 7 hyperedges and 1 with 8 hyperedges.
%p A059085 with(combinat): for n from 0 to 15 do printf(`%d,`,sum(stirling1(n,k)*2^(2^k), k=0..n)) od:
%Y A059085 Cf. A059084, A059086, A059087-A059089.
%K A059085 easy,nonn
%O A059085 0,1
%A A059085 Goran Kilibarda, _Vladeta Jovovic_, Dec 27 2000
%E A059085 More terms from _James Sellers_, Jan 24 2001