A392683 a(n) is the number of n-element families of nonempty subsets of {1, ..., n} in which every number in 1..n appears the same nonzero number of times.

1, 1, 5, 47, 1201, 96467, 22683315

Offset

1,3

Links

Table of n, a(n) for n=1..7.

Jason Zimba, Holiday Card Problem.

Example

a(3) = 5 because of:
  {{1}, {2}, {3}},
  {{1}, {2,3}, {1,2,3}},
  {{2}, {1,3}, {1,2,3}},
  {{3}, {1,2}, {1,2,3}},
  {{1,2}, {1,3}, {2,3}}.
These are the 5 three-element families of nonempty subsets of {1, 2, 3} in which every number in 1..3 appears the same nonzero number of times.

Mathematica

n = 5;
univ = Subsets[Subsets[Range[1, n], {1, n}], {n}];
balQ[flatset_] := Length[Union[flatset]] == n && Length[Union[Transpose[Tally[flatset]][[2]]]] == 1;
Length[Pick[univ, balQ/@(Flatten/@univ)]]

Crossrefs

Cf. A319190.

Sequence in context: A145564 A159480 A196460 * A093612 A069985 A300336

Adjacent sequences: A392680 A392681 A392682 * A392684 A392685 A392686

Keyword

nonn,more

Author

Jason Zimba, Jan 19 2026

Extensions

a(7) from Michael S. Branicky, Jan 20 2026

Status

approved