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 A362171 #14 Feb 01 2024 16:37:04
%S A362171 1,1,924,6358044,203356067376,23345633108619360,
%T A362171 7484535614458774428480,5583028528736289502562408256,
%U A362171 8547031978688473343843434600852224,24503310825110075324451531207978424853568,122607946140627185219752569884701085604290069760
%N A362171 a(n) = the hypergraph Catalan number C_6(n).
%C A362171 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 = 6.
%C A362171 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 A362171 Andrew Howroyd, <a href="/A362171/b362171.txt">Table of n, a(n) for n = 0..100</a>
%H A362171 Paul E. Gunnells, <a href="https://arxiv.org/abs/2102.05121">Generalized Catalan numbers from hypergraphs</a>, arXiv:2102.05121 [math.CO], 2021.
%F A362171 a(n) ~ sqrt(3)/2 * (6^5/5!)^n * n!^5/(Pi*n)^(5/2) (conjectural)
%Y A362171 Column k=6 of A369288.
%Y A362171 Cf. A000055, A000108, A362167, A362168, A362169, A362170, A362172.
%K A362171 nonn,walk
%O A362171 0,3
%A A362171 _Peter Bala_, Apr 10 2023
%E A362171 a(6) onwards from _Andrew Howroyd_, Feb 01 2024