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A059584 Triangle T(n,m) of number of labeled m-node T_0-hypergraphs with n hyperedges (empty hyperedges and multiple hyperedges included), m=0,1,...,2^n. 3
1, 1, 1, 2, 2, 1, 3, 7, 12, 12, 1, 4, 16, 68, 292, 1120, 3360, 6720, 6720, 1, 5, 30, 235, 2251, 23520, 245280, 2412480, 21631680, 172972800, 1210809600, 7264857600, 36324288000, 145297152000, 435891456000, 871782912000, 871782912000 (list; graph; refs; listen; history; text; 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

Table of n, a(n) for n=0..35.

FORMULA

T(n,m) = Sum_{i=0..m} stirling1(m, i)*binomial(2^i+n-1, n).

EXAMPLE

Triangle starts:

1, 1;

1, 2, 2;

1, 3, 7, 12, 12;

1, 4, 16, 68, 292, 1120, 3360, 6720, 6720;

...

There are 7 2-node T_0-hypergraphs with 2 hyperedges: {{}, {1}}, {{}, {2}}, {{1}, {1}}, {{1}, {2}}, {{1}, {1, 2}}, {{2}, {2}} and {{2}, {1, 2}}.

CROSSREFS

Cf. A059084, A051362 (=T(n,2)), A059585 (=T(n,3)), A059586 (row sums).

Sequence in context: A144304 A122941 A297622 * A295736 A136203 A113326

Adjacent sequences:  A059581 A059582 A059583 * A059585 A059586 A059587

KEYWORD

easy,nonn,tabf

AUTHOR

Vladeta Jovovic, Goran Kilibarda, Jan 23 2001

STATUS

approved

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Last modified January 22 15:13 EST 2022. Contains 350481 sequences. (Running on oeis4.)