A059088 - OEIS

%I #11 Oct 06 2017 19:49:07

%S 1,2,6,108,32076,2147160096,9223372004645279520,

%T 170141183460469231537996491317719562880,

%U 57896044618658097711785492504343953921871039195927143534211473291570199939840

%N Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge excluded).

%C 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 <a href="/A059087/a059087.pdf">Illustration of initial terms of A059087, A059088</a>

%F Row sums of A059087.

%F a(n) = A059085(n)/2.

%F a(n) = Sum_{k=0..n} stirling1(n, k)*2^((2^k)-1).

%e 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 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 Table[Sum[StirlingS1[n, k]*2^((2^k)-1), {k,0,n}], {n,0,10}] (* _G. C. Greubel_, Oct 06 2017 *)

%Y Cf. A059084-A059087, A059089.

%K easy,nonn

%O 0,2

%A Goran Kilibarda, _Vladeta Jovovic_, Dec 27 2000

%E More terms from _James A. Sellers_, Jan 24 2001