A059089 Number of labeled T_0-hypergraphs with n distinct hyperedges (empty hyperedge excluded).

2, 3, 27, 18209, 2369751602470, 5960531437867327674538684858601298, 479047836152505670895481842190009123676957243077039687942939196956404642582185242435050

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)=27; There are 27 labeled T_0-hypergraphs with 2 distinct hyperedges (empty hyperedge excluded): 3 2-node hypergraphs, 12 3-node hypergraphs and 12 4-node hypergraphs.
a(3) = (1/3!)*(-6*[1!*e]+11*[2!*e]-6*[4!*e]+[8!*e]) = (1/3!)*(-6*2+11*5-6*65+109601) = 18209, where [k!*e] := floor(k!*exp(1)).
		

Crossrefs

Cf. A059084-A059088.

Programs

Maple

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

Formula

Column sums of A059087.

a(n) = Sum_{k = 0..n} (-1)^(n-k)*A059086(k); a(n) = (1/n!)*Sum_{k = 0..n+1} stirling1(n+1, k)*floor(( 2^(k-1))!*exp(1)).

Extensions

More terms from James Sellers, Jan 24 2001