This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A362168 #17 Feb 01 2024 16:37:22
%S A362168 1,1,20,860,57200,5344800,682612800,118180104000,27396820448000,
%T A362168 8312583863720000,3209035788149600000,1534218535286625760000,
%U A362168 888028389273314675200000,611029957551257895664000000,492466785518772137553984000000,459270692175324078697443840000000
%N A362168 a(n) = the hypergraph Catalan number C_3(n).
%C A362168 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 = 3.
%C A362168 Gunnells gives several combinatorial interpretations of the hypergraph Catalan numbers, a method to compute their generating functions to arbitrary precision and some conjectural asymptotics.
%H A362168 Andrew Howroyd, <a href="/A362168/b362168.txt">Table of n, a(n) for n = 0..200</a>
%H A362168 Paul E. Gunnells, <a href="https://arxiv.org/abs/2102.05121">Generalized Catalan numbers from hypergraphs</a>, arXiv:2102.05121 [math.CO], 2021.
%F A362168 a(n) ~ sqrt(3) * (9/2)^n * n!^2/(Pi*n) (conjectural).
%o A362168 (PARI) Vec(HypCatColGf(3,15)) \\ HypCatColGf defined in A369288. - _Andrew Howroyd_, Feb 01 2024
%Y A362168 Column k=3 of A369288.
%Y A362168 Cf. A000055, A000108, A362167, A362169, A362170, A362171, A362172.
%K A362168 nonn,walk
%O A362168 0,3
%A A362168 _Peter Bala_, Apr 10 2023
%E A362168 a(9) onwards from _Andrew Howroyd_, Feb 01 2024