A051240 Number of 4-uniform hypergraphs on n unlabeled nodes, or equivalently pure 3-dimensional simplicial complexes on n unlabeled nodes.

1, 1, 1, 1, 2, 6, 156, 7013320, 29281354514767168, 234431745534048922731115555415680, 453456943706240925312368435237969462391555337386758635520

Offset: 0

Author

Vladeta Jovovic

Keywords

• nonn
• nice

References

• V. Jovovic, On the number of m-place relations (in Russian), Logiko-algebraicheskie konstruktsii, Tver, 1992, 59-66.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..18 (terms n=1..16 from Andrew Howroyd)
• E. M. Palmer, On the number of n-plexes, Discrete Math., 6 (1973), 377-390. [The numbers are incorrect]

Crossrefs

Cf. A000665, A092337, A301922.

Column k=4 of A309858.

Formula

a(n) = 1 + Sum_{i=1..n} A301922(i, 4). - Andrew Howroyd, Aug 09 2019

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 20 2019