A059085 Number of labeled n-node T_0-hypergraphs without multiple hyperedges (empty hyperedge included).

2, 4, 12, 216, 64152, 4294320192, 18446744009290559040, 340282366920938463075992982635439125760, 115792089237316195423570985008687907843742078391854287068422946583140399879680

Offset

0,1

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..8.

V. Jovovic, Illustration of initial terms of A059084, A059085

Formula

Row sums of A059084.

a(n) = Sum_{k=0..n} stirling1(n, k)*2^(2^k).

E.g.f.: Sum(2^(2^n)*log(1+x)^n/n!, n=0..infinity) = Sum(log(2)^n*(1+x)^(2^n)/n!, n=0..infinity). - Vladeta Jovovic, May 10 2004

Example

There are 216 labeled 3-node T_0-hypergraphs without multiple hyperedges (empty hyperedge included): 12 with 2 hyperedges, 44 with 3 hyperedges,67 with 4 hyperedges, 56 with 5 hyperedges, 28 with 6 hyperedges, 8 with 7 hyperedges and 1 with 8 hyperedges.

Maple

with(combinat): for n from 0 to 15 do printf(`%d, `, sum(stirling1(n, k)*2^(2^k), k=0..n)) od:

Crossrefs

Cf. A059084, A059086, A059087-A059089.

Sequence in context: A154734 A291827 A287059 * A030064 A224886 A180500

Adjacent sequences: A059082 A059083 A059084 * A059086 A059087 A059088

Keyword

easy,nonn

Author

Goran Kilibarda, Vladeta Jovovic, Dec 27 2000

Extensions

More terms from James A. Sellers, Jan 24 2001

Status

approved