A300913 Number of non-isomorphic connected set-systems of weight n.

1, 1, 1, 2, 4, 7, 18, 37, 96, 239, 658, 1810, 5358, 16057, 50373, 161811, 536964, 1826151, 6380481, 22822280, 83587920, 312954111, 1197178941, 4674642341, 18620255306, 75606404857, 312763294254, 1317356836235, 5646694922172, 24618969819915, 109125629486233, 491554330852608

Offset: 0

Author

Gus Wiseman, Jun 19 2018

Keywords

• nonn

Comments

The weight of a set-system is the sum of cardinalities of the sets. Weight is generally not the same as number of vertices.

Examples

			Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set systems:
1: {{1}}
2: {{1,2}}
3: {{1,2,3}}
   {{2},{1,2}}
4: {{1,2,3,4}}
   {{3},{1,2,3}}
   {{1,3},{2,3}}
   {{1},{2},{1,2}}
5: {{1,2,3,4,5}}
   {{4},{1,2,3,4}}
   {{1,4},{2,3,4}}
   {{2,3},{1,2,3}}
   {{2},{3},{1,2,3}}
   {{2},{1,3},{2,3}}
   {{3},{1,3},{2,3}}
Non-isomorphic representatives of the a(6) = 18 connected set-systems:
  {{1,2,3,4,5,6}}
  {{5},{1,2,3,4,5}}
  {{1,5},{2,3,4,5}}
  {{3,4},{1,2,3,4}}
  {{1,2,5},{3,4,5}}
  {{1,3,4},{2,3,4}}
  {{1},{1,4},{2,3,4}}
  {{1},{2,3},{1,2,3}}
  {{3},{4},{1,2,3,4}}
  {{3},{1,4},{2,3,4}}
  {{3},{2,3},{1,2,3}}
  {{4},{1,4},{2,3,4}}
  {{1,2},{1,3},{2,3}}
  {{1,3},{2,4},{3,4}}
  {{1,4},{2,4},{3,4}}
  {{1},{2},{3},{1,2,3}}
  {{1},{2},{1,3},{2,3}}
  {{2},{3},{1,3},{2,3}}
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 0..50 [using Andrew Howroyd's b-file for A283877]

Crossrefs

Cf. A007716, A055621, A283877, A293606, A293607.

Programs

Mathematica

A283877 = Import["https://oeis.org/A283877/b283877.txt", "Table"][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{1} ~Join~ EulerInvTransform[A283877 // Rest] (* Jean-François Alcover, Nov 07 2019, updated Mar 17 2020 *)

Formula

Inverse Euler transform of A283877.

Extensions

a(11)-a(31) from Jean-François Alcover, Nov 07 2019