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 A362169 #17 Feb 01 2024 16:37:18
%S A362169 1,1,70,15225,7043750,6327749750,10411817136000,29034031694460625,
%T A362169 126890003304310093750,816448082514611102718750,
%U A362169 7379204202189710013311562500,90369225128606332243844280406250,1457163640851863433667228849319062500,30217741884769257764596041337071409375000
%N A362169 a(n) = the hypergraph Catalan number C_4(n).
%C A362169 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.
%C A362169 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 A362169 Andrew Howroyd, <a href="/A362169/b362169.txt">Table of n, a(n) for n = 0..100</a>
%H A362169 Paul E. Gunnells, <a href="https://arxiv.org/abs/2102.05121">Generalized Catalan numbers from hypergraphs</a>, arXiv:2102.05121 [math.CO], 2021.
%F A362169 a(n) ~ sqrt(2) * (32/3)^n * n!^3/(Pi*n)^(3/2) (conjectural).
%o A362169 (PARI) Vec(HypCatColGf(4,15)) \\ HypCatColGf defined in A369288. - _Andrew Howroyd_, Feb 01 2024
%Y A362169 Column k=4 of A369288.
%Y A362169 Cf. A000055, A000108, A362167, A362168, A362170, A362171, A362172.
%K A362169 nonn,walk
%O A362169 0,3
%A A362169 _Peter Bala_, Apr 10 2023
%E A362169 a(8) onwards from _Andrew Howroyd_, Feb 01 2024