A059523 Number of n-element unlabeled ordered T_0-antichains without isolated vertices; number of T_1-hypergraphs (without empty edge and without multiple edges) on n labeled vertices.

1, 2, 2, 36, 19020, 2010231696, 9219217412568364176, 170141181796805105960861096082778425120, 57896044618658097536026644159052312977171804852352892309392604715987334365792

Offset: 0

Author

Vladeta Jovovic and Goran Kilibarda, Jan 20 2001; revised Jun 03 2004

Keywords

• nonn

Examples

			Number of k-element T_1-hipergraphs (without empty edge and without multiple edges) on 3 labeled vertices is
C(7,k)-6*C(5,k)+6*C(4,k)+3*C(3,k)-6*C(2,k)+2*C(1,k),k=0..7; so a(3)=2+11+15+7+1=36=2^7-6*2^5+6*2^4+3*2^3-6*2^2+2*2.
		

Links

• V. Jovovic, T_1-hyper graphs on a labeled 3-set
• Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
• Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.

Crossrefs

Cf. A003465, A059201, A059052, A326961.

Formula

a(n) = A059052(n)/2.