A059088 Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge excluded).

1, 2, 6, 108, 32076, 2147160096, 9223372004645279520, 170141183460469231537996491317719562880, 57896044618658097711785492504343953921871039195927143534211473291570199939840

Offset: 0

Author

Goran Kilibarda, Vladeta Jovovic, Dec 27 2000

Keywords

• easy
• nonn

Comments

A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.

Examples

			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.
		

Links

• Illustration of initial terms of A059087, A059088

Crossrefs

Cf. A059084-A059087, A059089.

Programs

Maple

with(combinat): for n from 0 to 15 do printf(`%d,`,(1/2)*sum(stirling1(n,k)*2^(2^k), k= 0..n)) od:

Mathematica

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

Formula

Row sums of A059087.

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

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

Extensions

More terms from James Sellers, Jan 24 2001