A306020 - OEIS

%I #22 Sep 13 2023 23:18:52

%S 1,2,5,16,95,2110,1114237,68723671292,1180735735906024030715,

%T 170141183460507917357914971986913657850,

%U 7237005577335553223087828975127304179197147198604070555943173844710572689401

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

%C A058673(n) <= a(n). - _Lorenzo Sauras Altuzarra_, Aug 10 2023

%H <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>

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

%e a(3) = 16 set-systems in which all sets have the same size:

%e   {}

%e   {{1}}

%e   {{2}}

%e   {{3}}

%e   {{1,2}}

%e   {{1,3}}

%e   {{2,3}}

%e   {{1,2,3}}

%e   {{1},{2}}

%e   {{1},{3}}

%e   {{2},{3}}

%e   {{1,2},{1,3}}

%e   {{1,2},{2,3}}

%e   {{1,3},{2,3}}

%e   {{1},{2},{3}}

%e   {{1,2},{1,3},{2,3}}

%p a := n -> 1-n+add(2^binomial(n, d), d = 1 .. n):

%p seq(a(n), n = 0 .. 10); # _Lorenzo Sauras Altuzarra_, Aug 11 2023

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

%o (PARI) a(n) = 1 - n + sum(d = 1, n, 2^binomial(n, d)); \\ _Michel Marcus_, Aug 10 2023

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

%K nonn

%O 0,2

%A _Gus Wiseman_, Jun 17 2018