A326907 - OEIS

%I #8 Aug 11 2019 12:24:35

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

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

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

%e Non-isomorphic representatives of the a(0) = 2 through a(3) = 28 sets of sets:

%e   {}    {{1}}    {{12}}          {{123}}

%e   {{}}  {{}{1}}  {{}{12}}        {{}{123}}

%e                  {{2}{12}}       {{3}{123}}

%e                  {{}{2}{12}}     {{23}{123}}

%e                  {{1}{2}{12}}    {{}{3}{123}}

%e                  {{}{1}{2}{12}}  {{}{23}{123}}

%e                                  {{1}{23}{123}}

%e                                  {{3}{23}{123}}

%e                                  {{13}{23}{123}}

%e                                  {{}{1}{23}{123}}

%e                                  {{}{3}{23}{123}}

%e                                  {{}{13}{23}{123}}

%e                                  {{2}{3}{23}{123}}

%e                                  {{2}{13}{23}{123}}

%e                                  {{3}{13}{23}{123}}

%e                                  {{12}{13}{23}{123}}

%e                                  {{}{2}{3}{23}{123}}

%e                                  {{}{2}{13}{23}{123}}

%e                                  {{}{3}{13}{23}{123}}

%e                                  {{}{12}{13}{23}{123}}

%e                                  {{2}{3}{13}{23}{123}}

%e                                  {{3}{12}{13}{23}{123}}

%e                                  {{}{2}{3}{13}{23}{123}}

%e                                  {{}{3}{12}{13}{23}{123}}

%e                                  {{2}{3}{12}{13}{23}{123}}

%e                                  {{}{2}{3}{12}{13}{23}{123}}

%e                                  {{1}{2}{3}{12}{13}{23}{123}}

%e                                  {{}{1}{2}{3}{12}{13}{23}{123}}

%Y The case without empty sets is A108798.

%Y The case with a single covering edge is A108800.

%Y First differences of A193675.

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

%Y The labeled version is A326906.

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

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

%K nonn,more

%O 0,1

%A _Gus Wiseman_, Aug 03 2019

%E a(7) added from A108800 by _Andrew Howroyd_, Aug 10 2019