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A306020
a(n) is the number of set-systems using nonempty subsets of {1,...,n} in which all sets have the same size.
10
1, 2, 5, 16, 95, 2110, 1114237, 68723671292, 1180735735906024030715, 170141183460507917357914971986913657850, 7237005577335553223087828975127304179197147198604070555943173844710572689401
OFFSET
0,2
COMMENTS
A058673(n) <= a(n). - Lorenzo Sauras Altuzarra, Aug 10 2023
FORMULA
a(n) = 1 - n + Sum_{d = 1..n} 2^binomial(n, d).
EXAMPLE
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}}
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}]
PROG
(PARI) a(n) = 1 - n + sum(d = 1, n, 2^binomial(n, d)); \\ Michel Marcus, Aug 10 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 17 2018
STATUS
approved