A301481 - OEIS

%I #28 Aug 21 2019 05:31:57

%S 1,1,2,4,12,58,2381,14026281,29284932065996445,

%T 468863491068204425232922367150021,

%U 1994324729204021501147398087008429476673379600542622915802043462326345

%N Number of unlabeled uniform hypergraphs spanning n vertices.

%C A hypergraph is uniform if all edges have the same size.

%H Alois P. Heinz, <a href="/A301481/b301481.txt">Table of n, a(n) for n = 0..14</a> (first 13 terms from Andrew Howroyd)

%e Non-isomorphic representatives of the a(4) = 12 hypergraphs:

%e   {{1,2,3,4}}

%e   {{1,2},{3,4}}

%e   {{1},{2},{3},{4}}

%e   {{1,3,4},{2,3,4}}

%e   {{1,3},{2,4},{3,4}}

%e   {{1,4},{2,4},{3,4}}

%e   {{1,2,4},{1,3,4},{2,3,4}}

%e   {{1,2},{1,3},{2,4},{3,4}}

%e   {{1,4},{2,3},{2,4},{3,4}}

%e   {{1,3},{1,4},{2,3},{2,4},{3,4}}

%e   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}

%e   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

%o (PARI) \\ see A301922 for U(n,k).

%o a(n)={ if(n==0, 1, sum(k=1, n, U(n,k)-U(n-1,k))) } \\ _Andrew Howroyd_, Aug 10 2019

%Y Row sums of A301922.

%Y Cf. A003465, A038041, A055621, A298422, A301920, A306017-A306021.

%K nonn

%O 0,3

%A _Gus Wiseman_, Jun 19 2018

%E Terms a(6) and beyond from _Andrew Howroyd_, Aug 09 2019