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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. 9
1, 2, 5, 16, 95, 2110, 1114237, 68723671292, 1180735735906024030715, 170141183460507917357914971986913657850, 7237005577335553223087828975127304179197147198604070555943173844710572689401 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..10.

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}}

MATHEMATICA

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

CROSSREFS

Cf. A000005, A001315, A007716, A038041, A049311, A283877, A298422, A306017, A306018, A306019, A306021.

Sequence in context: A048754 A176343 A327062 * A037075 A115894 A033835

Adjacent sequences:  A306017 A306018 A306019 * A306021 A306022 A306023

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 17 2018

STATUS

approved

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Last modified October 21 21:45 EDT 2019. Contains 328315 sequences. (Running on oeis4.)