The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A306021 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A306021

Number of set-systems spanning {1,...,n} in which all sets have the same size.
(history; published version)

#22 by OEIS Server at Tue Jan 16 22:05:39 EST 2024

LINKS

Andrew Howroyd, <a href="/A306021/b306021_1.txt">Table of n, a(n) for n = 0..14</a>

#21 by Michael De Vlieger at Tue Jan 16 22:05:39 EST 2024

STATUS

proposed

approved

Discussion

Tue Jan 16

22:05

OEIS Server: Installed first b-file as b306021.txt.

#20 by Jon E. Schoenfield at Tue Jan 16 20:54:48 EST 2024

STATUS

editing

proposed

#19 by Jon E. Schoenfield at Tue Jan 16 20:54:46 EST 2024

EXAMPLE

{{1,2,3}}

{{1}, {2}, {3}}

{{1,2}, {1,3}}

{{1,2}, {2,3}}

{{1,3}, {2,3}}

{{1,2}, {1,3}, {2,3}}

STATUS

proposed

editing

#18 by Andrew Howroyd at Tue Jan 16 20:40:15 EST 2024

STATUS

editing

proposed

#17 by Andrew Howroyd at Tue Jan 16 20:38:14 EST 2024

CROSSREFS

The connected version is A299353.

#16 by Andrew Howroyd at Tue Jan 16 20:31:57 EST 2024

FORMULA

Inverse binomial transform of A306020. - Andrew Howroyd, Jan 16 2024

#15 by Andrew Howroyd at Tue Jan 16 20:08:55 EST 2024

COMMENTS

a(n) is the number of labeled uniform hypergraphs spanning n vertices. - Andrew Howroyd, Jan 16 2024

LINKS

Andrew Howroyd, <a href="/A306021/b306021_1.txt">Table of n, a(n) for n = 0..14</a>

PROG

(PARI) a(n) = if(n==0, 1, sum(k=0, n, sum(d=0, n, (-1)^(n-d)*binomial(n, d)*2^binomial(d, k)))) \\ Andrew Howroyd, Jan 16 2024

CROSSREFS

Row sums of A299471.

The unlabeled version is A301481.

STATUS

approved

editing

#14 by Alois P. Heinz at Sun Jan 22 18:20:12 EST 2023

STATUS

proposed

approved

#13 by Jon E. Schoenfield at Sun Jan 22 17:24:53 EST 2023

STATUS

editing

proposed