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%I M1723 #19 Aug 20 2019 09:41:04
%S 1,1,1,1,2,6,156,7013320,29281354514767168,
%T 234431745534048922731115555415680,
%U 453456943706240925312368435237969462391555337386758635520
%N Number of 4-uniform hypergraphs on n unlabeled nodes, or equivalently pure 3-dimensional simplicial complexes on n unlabeled nodes.
%D V. Jovovic, On the number of m-place relations (in Russian), Logiko-algebraicheskie konstruktsii, Tver, 1992, 59-66.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A051240/b051240.txt">Table of n, a(n) for n = 0..18</a> (terms n=1..16 from Andrew Howroyd)
%H E. M. Palmer, <a href="http://dx.doi.org/10.1016/0012-365X(73)90069-1">On the number of n-plexes</a>, Discrete Math., 6 (1973), 377-390. [The numbers are incorrect]
%F a(n) = 1 + Sum_{i=1..n} A301922(i, 4). - _Andrew Howroyd_, Aug 09 2019
%Y Cf. A000665, A092337, A301922.
%Y Column k=4 of A309858.
%K nonn,nice
%O 0,5
%A _Vladeta Jovovic_
%E a(0)=1 prepended by _Alois P. Heinz_, Aug 20 2019
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