A306020 a(n) is the number of set-systems using nonempty subsets of {1,...,n} in which all sets have the same size.

1, 2, 5, 16, 95, 2110, 1114237, 68723671292, 1180735735906024030715, 170141183460507917357914971986913657850, 7237005577335553223087828975127304179197147198604070555943173844710572689401

Offset: 0

Author

Gus Wiseman, Jun 17 2018

Keywords

• nonn

Comments

A058673(n) <= a(n). - Lorenzo Sauras Altuzarra, Aug 10 2023

Examples

			a(3) = 16 set-systems in which all sets have the same size:
  {}
  {{1}}
  {{2}}
  {{3}}
  {{1,2}}
  {{1,3}}
  {{2,3}}
  {{1,2,3}}
  {{1},{2}}
  {{1},{3}}
  {{2},{3}}
  {{1,2},{1,3}}
  {{1,2},{2,3}}
  {{1,3},{2,3}}
  {{1},{2},{3}}
  {{1,2},{1,3},{2,3}}
		

Links

• Index entries for sequences related to matroids

Crossrefs

Cf. A000005, A001315, A007716, A038041, A049311, A058673 (labeled matroids), A283877, A298422, A306017, A306018, A306019, A306021.

Row sums of A059328.

Programs

Maple

a := n -> 1-n+add(2^binomial(n, d), d = 1 .. n):
seq(a(n), n = 0 .. 10); # Lorenzo Sauras Altuzarra, Aug 11 2023

Mathematica

Table[1+Sum[2^Binomial[n,d]-1,{d,n}],{n,10}]

PARI

a(n) = 1 - n + sum(d = 1, n, 2^binomial(n, d)); \\ Michel Marcus, Aug 10 2023

Formula

a(n) = 1 - n + Sum_{d = 1..n} 2^binomial(n, d).