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%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
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