login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059086 Number of labeled T_0-hypergraphs with n distinct hyperedges (empty hyperedge included). 7
2, 5, 30, 18236, 2369751620679, 5960531437867327674541054610203768, 479047836152505670895481842190009123676957243077039693903470634823732317120870101036348 (list; graph; refs; listen; history; text; internal format)
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(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)).

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:

CROSSREFS

Column sums of A059084.

Cf. A059084, A059085, A059087-A059089.

Sequence in context: A275255 A219273 A000133 * A215168 A266478 A107389

Adjacent sequences:  A059083 A059084 A059085 * A059087 A059088 A059089

KEYWORD

easy,nonn

AUTHOR

Goran Kilibarda, Vladeta Jovovic, Dec 27 2000

EXTENSIONS

More terms from James A. Sellers, Jan 24 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 14 03:43 EDT 2022. Contains 356110 sequences. (Running on oeis4.)