A306021 Number of set-systems spanning {1,...,n} in which all sets have the same size.

1, 1, 2, 6, 54, 1754, 1102746, 68715913086, 1180735735356265746734, 170141183460507906731293351306656207090, 7237005577335553223087828975127304177495735363998991435497132232365910414322

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