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 A059586 #9 Jul 02 2025 16:02:00
%S A059586 2,5,35,18301,2369751675482,5960531437867327674550533616796025,
%T A059586 479047836152505670895481842190009123676957243077039723706127824160370689849840668444493
%N A059586 Number of labeled T_0-hypergraphs with n hyperedges (empty hyperedges and multiple hyperedges included).
%C A059586 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 A059586 a(n)=(1/n!)*Sum_{k=0..n} |stirling1(n, k)|*floor((2^k)!*exp(1)).
%e A059586 a(3) = (1/3!) * (2 * [2! * e] + 3 * [4! * e] + [8! * e]) = (1/3!) * (2 * 5 + 3 * 65 + 109601) = 18301, where [k! * e] := floor(k! * exp(1)).
%p A059586 with(combinat): Digits := 1000: f := n->(1/n!)*sum(abs(stirling1(n,i))*floor((2^i)!*exp(1)), i=0..n): for n from 0 to 8 do printf(`%d,`,f(n)) od:
%Y A059586 Cf. A000522, A059086, A059584, A059585.
%K A059586 easy,nonn
%O A059586 0,1
%A A059586 _Vladeta Jovovic_, Goran Kilibarda, Jan 23 2001
%E A059586 More terms from _James Sellers_, Jan 24 2001