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A059088 Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge excluded). 5
1, 2, 6, 108, 32076, 2147160096, 9223372004645279520, 170141183460469231537996491317719562880, 57896044618658097711785492504343953921871039195927143534211473291570199939840 (list; graph; refs; listen; history; text; 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
FORMULA
Row sums of A059087.
a(n) = A059085(n)/2.
a(n) = 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:
MATHEMATICA
Table[Sum[StirlingS1[n, k]*2^((2^k)-1), {k, 0, n}], {n, 0, 10}] (* G. C. Greubel, Oct 06 2017 *)
CROSSREFS
Sequence in context: A181036 A222854 A351780 * A216151 A057771 A056164
KEYWORD
easy,nonn
AUTHOR
Goran Kilibarda, Vladeta Jovovic, Dec 27 2000
EXTENSIONS
More terms from James A. Sellers, Jan 24 2001
STATUS
approved

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Last modified February 25 06:40 EST 2024. Contains 370310 sequences. (Running on oeis4.)