A326907 Number of non-isomorphic sets of subsets of {1..n} that are closed under union and cover all n vertices. First differences of A193675.

2, 2, 6, 28, 330, 28960, 216562364, 5592326182940100

Offset: 0

Author

Gus Wiseman, Aug 03 2019

Keywords

• nonn
• more

Comments

Differs from A108800 in having a(0) = 2 instead of 1.

Examples

			Non-isomorphic representatives of the a(0) = 2 through a(3) = 28 sets of sets:
  {}    {{1}}    {{12}}          {{123}}
  {{}}  {{}{1}}  {{}{12}}        {{}{123}}
                 {{2}{12}}       {{3}{123}}
                 {{}{2}{12}}     {{23}{123}}
                 {{1}{2}{12}}    {{}{3}{123}}
                 {{}{1}{2}{12}}  {{}{23}{123}}
                                 {{1}{23}{123}}
                                 {{3}{23}{123}}
                                 {{13}{23}{123}}
                                 {{}{1}{23}{123}}
                                 {{}{3}{23}{123}}
                                 {{}{13}{23}{123}}
                                 {{2}{3}{23}{123}}
                                 {{2}{13}{23}{123}}
                                 {{3}{13}{23}{123}}
                                 {{12}{13}{23}{123}}
                                 {{}{2}{3}{23}{123}}
                                 {{}{2}{13}{23}{123}}
                                 {{}{3}{13}{23}{123}}
                                 {{}{12}{13}{23}{123}}
                                 {{2}{3}{13}{23}{123}}
                                 {{3}{12}{13}{23}{123}}
                                 {{}{2}{3}{13}{23}{123}}
                                 {{}{3}{12}{13}{23}{123}}
                                 {{2}{3}{12}{13}{23}{123}}
                                 {{}{2}{3}{12}{13}{23}{123}}
                                 {{1}{2}{3}{12}{13}{23}{123}}
                                 {{}{1}{2}{3}{12}{13}{23}{123}}
		

Crossrefs

The case without empty sets is A108798.

The case with a single covering edge is A108800.

First differences of A193675.

The case also closed under intersection is A326898 for n > 0.

The labeled version is A326906.

The same for union instead of intersection is (also) A326907.

Cf. A001930, A102895, A108798, A193674, A193675, A326880, A326881, A326883, A326898, A326908.

Extensions

a(7) added from A108800 by Andrew Howroyd, Aug 10 2019