A059086 Number of labeled T_0-hypergraphs with n distinct hyperedges (empty hyperedge included).

2, 5, 30, 18236, 2369751620679, 5960531437867327674541054610203768, 479047836152505670895481842190009123676957243077039693903470634823732317120870101036348

Offset: 0

Author

Goran Kilibarda, Vladeta Jovovic, Dec 27 2000

Keywords

• easy
• nonn

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.

Examples

			a(2)=30; There are 30 labeled T_0-hypergraphs with 2 distinct hyperedges (empty hyperedge included): 1 1-node hypergraph, 5 2-node hypergraphs, 12 3-node hypergraphs and 12 4-node hypergraphs.
a(3) = (1/3!)*(2*[2!*e]-3*[4!*e]+[8!*e]) = (1/3!)*(2*5-3*65+109601) = 18236, where [k!*e] := floor (k!*exp(1)).
		

Crossrefs

Column sums of A059084.

Cf. A059084, A059085, A059087-A059089.

Programs

Maple

with(combinat): Digits := 1000: for n from 0 to 8 do printf(`%d,`,(1/n!)*sum(stirling1(n, k)*floor((2^k)!*exp(1)), k=0..n)) od:

Formula

a(n) = (1/n!)*Sum_{k = 0..n} stirling1(n, k)*floor((2^k)!*exp(1)).

Extensions

More terms from James Sellers, Jan 24 2001