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 A341854 #16 Jul 31 2024 10:00:34
%S A341854 14,84,504,3192,21252,147420,1057224,7791168,58727214,451137596,
%T A341854 3521923944,27878644080,223353322920,1808402199660,14778966163752,
%U A341854 121784464712064,1011022286145816,8449458780183120,71042841567457760,600615322603936920,5103281457829103220
%N A341854 Number of triangulations of a fixed hexagon with n internal nodes.
%C A341854 These may be called rooted [n,3] triangulations.
%H A341854 Andrew Howroyd, <a href="/A341854/b341854.txt">Table of n, a(n) for n = 0..500</a>
%H A341854 K. A. Penson, K. Górska, A. Horzela, and G. H. E. Duchamp, <a href="https://arxiv.org/abs/2209.06574">Hausdorff moment problem for combinatorial numbers of Brown and Tutte: exact solution</a>, arXiv:2209.06574 [math.CO], 2022.
%F A341854 a(n) = 1008*binomial(4*n+7, n)/((3*n+8)*(3*n+9)).
%F A341854 D-finite with recurrence 3*(3*n+7)*(n+3)*(3*n+8)*a(n) +(-445*n^3-2164*n^2-3473*n-1838)*a(n-1) +56*(4*n+1)*(2*n+1)*(4*n+3)*a(n-2)=0. - _R. J. Mathar_, Jul 31 2024
%F A341854 D-finite with recurrence 3*n*(3*n+7)*(n+3)*(3*n+8)*a(n) -8*(4*n+5)*(2*n+3)*(4*n+7)*(n+1)*a(n-1)=0. - _R. J. Mathar_, Jul 31 2024
%t A341854 Array[1008 Binomial[4 # + 7, #]/((3 # + 8) (3 # + 9)) &, 21, 0] (* _Michael De Vlieger_, Feb 22 2021 *)
%o A341854 (PARI) a(n) = {1008*binomial(4*n+7, n)/((3*n+8)*(3*n+9))}
%Y A341854 Column k=3 of A146305.
%K A341854 nonn
%O A341854 0,1
%A A341854 _Andrew Howroyd_, Feb 21 2021