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 A362172 a(n) = the hypergraph Catalan number C_7(n). 9
 1, 1, 3432, 141858288, 40309820014464, 53321581727982247680, 238681094467043912358445056 (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 = 7. 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..6. Paul E. Gunnells, Generalized Catalan numbers from hypergraphs, arXiv:2102.05121 [math.CO], 2021. FORMULA a(n) ~ sqrt(7)/4 * (7^6/6!)^n * n!^6/(Pi*n)^3 (conjectural). CROSSREFS Cf. A000055, A000108, A362167, A362168, A362169, A362170, A362171. Sequence in context: A177307 A140911 A351486 * A177308 A177309 A172603 Adjacent sequences: A362169 A362170 A362171 * A362173 A362174 A362175 KEYWORD nonn,walk,more AUTHOR Peter Bala, Apr 10 2023 STATUS approved

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Last modified December 7 09:30 EST 2023. Contains 367645 sequences. (Running on oeis4.)