|
| |
|
|
A059084
|
|
Triangle T(n,m) of number of labeled n-node T_0-hypergraphs with m distinct hyperedges (empty hyperedge included),m=0,1,...,2^n.
|
|
13
| |
|
|
1, 1, 1, 2, 1, 0, 2, 5, 4, 1, 0, 0, 12, 44, 67, 56, 28, 8, 1, 0, 0, 12, 268, 1411, 4032, 7840, 11392, 12864, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 1120, 20160, 159656, 827092, 3251736, 10389635, 27934400, 64432160, 128980800, 225774640
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
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
| V. Jovovic, Illustration of initial terms of A059084, A059085
|
|
|
FORMULA
| T(n, m)=Sum_{i=0..n} s(n, i)*binomial(2^i, m), where s(n, i) are Stirling numbers of the first kind.
Also T(n, m)=(1/m!)*Sum_{i=0..m} s(m, i)*fallfac(2^i, n). E.g.f: Sum((1+x)^(2^n)*ln(1+y)^n/n!, n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 19 2004
|
|
|
EXAMPLE
| [1,1],[1,2,1],[0,2,5,4,1],[0,0,12,44,67,56,28,8,1],...; There are 12 labeled 3-node T_0-hypergraphs with 2 distinct hyperedges: {{3},{2}}, {{3},{2,3}}, {{2},{2,3}}, {{3},{1}}, {{3},{1,3}}, {{2},{1}}, {{2,3},{1,3}}, {{2},{1,2}}, {{2,3},{1,2}}, {{1},{1,3}}, {{1},{1,2}}, {{1,3},{1,2}}.
|
|
|
CROSSREFS
| Cf. A059085, A059086.
Cf. A088309.
Sequence in context: A147702 A118208 A074142 * A070677 A029584 A199469
Adjacent sequences: A059081 A059082 A059083 * A059085 A059086 A059087
|
|
|
KEYWORD
| easy,nonn,tabf
|
|
|
AUTHOR
| Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 27 2000
|
| |
|
|
