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A306021 Number of set-systems spanning {1,...,n} in which all sets have the same size. 41
1, 1, 2, 6, 54, 1754, 1102746, 68715913086, 1180735735356265746734, 170141183460507906731293351306656207090, 7237005577335553223087828975127304177495735363998991435497132232365910414322 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = Sum_{k = 0...n} (-1)^(n - k) binomial(n, k) (1 - k + Sum_{d = 1...k} 2^binomial(k, d)).

EXAMPLE

The a(3) = 6 set-systems in which all sets have the same size:

{{1,2,3}}

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

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

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

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

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

MATHEMATICA

Table[Sum[(-1)^(n-k)*Binomial[n, k]*(1+Sum[2^Binomial[k, d]-1, {d, k}]), {k, 0, n}], {n, 12}]

CROSSREFS

Cf. A000005, A001315, A007716, A038041, A049311, A283877, A298422, A306017, A306018, A306019, A306020.

Sequence in context: A085078 A152543 A279454 * A122593 A267348 A264610

Adjacent sequences:  A306018 A306019 A306020 * A306022 A306023 A306024

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 17 2018

STATUS

approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)