|
| |
|
|
A059088
|
|
Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge excluded).
|
|
3
| |
|
|
1, 2, 6, 108, 32076, 2147160096, 9223372004645279520, 170141183460469231537996491317719562880, 57896044618658097711785492504343953921871039195927143534211473291570199939840
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
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.
|
|
|
LINKS
| Illustration of initial terms of A059087, A059088
|
|
|
FORMULA
| Row sums of A059087. a(n)=A059085(n)/2.
a(n)=A059085(n)/2=Sum_{k=0..n} stirling1(n, k)*2^((2^k)-1).
|
|
|
EXAMPLE
| 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.
|
|
|
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:
|
|
|
CROSSREFS
| Cf. A059084-A059087, A059089.
Sequence in context: A054247 A099790 A181036 * A057771 A056164 A156500
Adjacent sequences: A059085 A059086 A059087 * A059089 A059090 A059091
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2000
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 24 2001
|
| |
|
|
