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 A362170 #15 Feb 01 2024 16:37:13
%S A362170 1,1,252,299880,1112865264,11126161436292,255654847841227632,
%T A362170 11676346013544951854304,953196481551725431240711680,
%U A362170 128864126679853773803689954958112,27235509875891350493949247236459319296,8599544533810439129313490410035564948257536
%N A362170 a(n) = the hypergraph Catalan number C_5(n).
%C A362170 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 = 5.
%C A362170 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 A362170 Andrew Howroyd, <a href="/A362170/b362170.txt">Table of n, a(n) for n = 0..100</a>
%H A362170 Paul E. Gunnells, <a href="https://arxiv.org/abs/2102.05121">Generalized Catalan numbers from hypergraphs</a>, arXiv:2102.05121 [math.CO], 2021.
%F A362170 a(n) ~ sqrt(5)/2 * (5^4/24)^n * n!^4/(Pi*n)^2 (conjectural).
%Y A362170 Column k=5 of A369288.
%Y A362170 Cf. A000055, A000108, A362167, A362168, A362169, A362171, A362172.
%K A362170 nonn,walk
%O A362170 0,3
%A A362170 _Peter Bala_, Apr 10 2023
%E A362170 a(7) onwards from _Andrew Howroyd_, Feb 01 2024