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 A362169 a(n) = the hypergraph Catalan number C_4(n). 5
 1, 1, 70, 15225, 7043750, 6327749750, 10411817136000, 29034031694460625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Let m >= 1. The sequence of hypergraph Catalan numbers {C_m(n): n >= 0} is defined in terms of counting walks on trees, weighted by the orders of their automorphism groups. See Gunnells. When m = 1 we get the sequence of Catalan numbers A000108. The present sequence is the case m = 4. Gunnells gives several combinatorial interpretations of the hypergraph Catalan numbers, a method to compute their generating functions to arbitrary precision and some conjectural asymptotics. LINKS Table of n, a(n) for n=0..7. Paul E. Gunnells, Generalized Catalan numbers from hypergraphs, arXiv:2102.05121 [math.CO], 2021. FORMULA a(n) ~ sqrt(2) * (32/3)^n * n!^3/(Pi*n)^(3/2) (conjectural). CROSSREFS Cf. A000055, A000108, A362167, A362168, A362170, A362171, A362172. Sequence in context: A330244 A362916 A229776 * A231054 A007100 A103157 Adjacent sequences: A362166 A362167 A362168 * A362170 A362171 A362172 KEYWORD nonn,walk,more AUTHOR Peter Bala, Apr 10 2023 STATUS approved

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Last modified October 3 19:07 EDT 2023. Contains 365870 sequences. (Running on oeis4.)