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 A370060 #14 Feb 08 2024 20:45:23
%S A370060 1,1,1,1,1,1,1,1,3,2,1,1,2,4,2,1,1,4,4,12,5,1,1,3,6,9,18,5,1,1,5,6,26,
%T A370060 22,55,14,1,1,4,8,21,45,52,88,14,1,1,6,8,45,51,204,140,273,42,1,1,5,
%U A370060 10,38,84,190,380,340,455,42,1,1,7,10,69,92,500,506,1771,969,1428,132
%N A370060 Array read by antidiagonals: T(n,k) is the number of achiral dissections of a polygon into n k-gons by nonintersecting diagonals rooted at a cell, n >= 1, k >= 3.
%C A370060 The polygon prior to dissection will have n*(k-2)+2 sides.
%H A370060 Andrew Howroyd, <a href="/A370060/b370060.txt">Table of n, a(n) for n = 1..1275</a> (first 50 antidiagonals)
%H A370060 F. Harary, E. M. Palmer and R. C. Read, <a href="http://dx.doi.org/10.1016/0012-365X(75)90041-2">On the cell-growth problem for arbitrary polygons</a>, Discr. Math. 11 (1975), 371-389.
%H A370060 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss%E2%80%93Catalan_number">Fuss-Catalan number</a>
%F A370060 T(n,k) = 2*A295259(n,k) - A295222(n,k).
%F A370060 T(n,2*k+1) = A370062(n,2*k+1).
%e A370060 Array begins:
%e A370060 =============================================
%e A370060 n\k| 3 4 5 6 7 8 9 10 ...
%e A370060 ---+-----------------------------------------
%e A370060 1 | 1 1 1 1 1 1 1 1 ...
%e A370060 2 | 1 1 1 1 1 1 1 1 ...
%e A370060 3 | 1 3 2 4 3 5 4 6 ...
%e A370060 4 | 2 4 4 6 6 8 8 10 ...
%e A370060 5 | 2 12 9 26 21 45 38 69 ...
%e A370060 6 | 5 18 22 45 51 84 92 135 ...
%e A370060 7 | 5 55 52 204 190 500 468 992 ...
%e A370060 8 | 14 88 140 380 506 1008 1240 2100 ...
%e A370060 9 | 14 273 340 1771 1950 6200 6545 15990 ...
%e A370060 ...
%o A370060 (PARI) \\ here u is Fuss-Catalan sequence with p = k-1.
%o A370060 u(n, k, r) = {r*binomial((k - 1)*n + r, n)/((k - 1)*n + r)}
%o A370060 T(n, k) = {if(k%2, if(n%2, u((n-1)/2, k, (k-1)/2), u(n/2-1, k, (k-1))), if(n%2, u((n-1)/2, k, k/2+1), u(n/2-1, k, k)) )}
%o A370060 for(n=1, 9, for(k=3, 10, print1(T(n, k), ", ")); print);
%Y A370060 Columns k=3..6 are A208355(n-1), A124817(n-1), A369472, A370061.
%Y A370060 Cf. A070914 (rooted), A295222 (oriented), A295259 (unoriented), A369929, A370062 (achiral unrooted).
%K A370060 nonn,tabl
%O A370060 1,9
%A A370060 _Andrew Howroyd_, Feb 08 2024