A059586 Number of labeled T_0-hypergraphs with n hyperedges (empty hyperedges and multiple hyperedges included).

2, 5, 35, 18301, 2369751675482, 5960531437867327674550533616796025, 479047836152505670895481842190009123676957243077039723706127824160370689849840668444493

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..6.

Formula

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

Example

a(3) = (1/3!) * (2 * [2! * e] + 3 * [4! * e] + [8! * e]) = (1/3!) * (2 * 5 + 3 * 65 + 109601) = 18301, where [k! * e] := floor(k! * exp(1)).

Maple

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

Crossrefs

Cf. A000522, A059086, A059584, A059585.

Sequence in context: A238752 A099137 A309667 * A160968 A329704 A275552

Adjacent sequences: A059583 A059584 A059585 * A059587 A059588 A059589

Keyword

easy,nonn

Author

Vladeta Jovovic, Goran Kilibarda, Jan 23 2001

Extensions

More terms from James A. Sellers, Jan 24 2001

Status

approved