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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.
16
1, 2, 2, 36, 19020, 2010231696, 9219217412568364176, 170141181796805105960861096082778425120, 57896044618658097536026644159052312977171804852352892309392604715987334365792
OFFSET
0,2
LINKS
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.
FORMULA
a(n) = A059052(n)/2.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic and Goran Kilibarda, Jan 20 2001; revised Jun 03 2004
STATUS
approved