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 A370062 #9 Feb 08 2024 20:45:27
%S A370062 1,1,1,1,1,1,1,1,2,2,1,1,2,3,2,1,1,3,4,7,5,1,1,3,5,9,12,5,1,1,4,6,18,
%T A370062 22,30,14,1,1,4,7,21,35,52,55,14,1,1,5,8,34,51,136,140,143,42,1,1,5,9,
%U A370062 38,70,190,285,340,273,42,1,1,6,10,55,92,368,506,1155,969,728,132
%N A370062 Array read by antidiagonals: T(n,k) is the number of achiral dissections of a polygon into n k-gons by nonintersecting diagonals, n >= 1, k >= 3.
%C A370062 The polygon prior to dissection will have n*(k-2)+2 sides.
%H A370062 Andrew Howroyd, <a href="/A370062/b370062.txt">Table of n, a(n) for n = 1..1275</a> (first 50 antidiagonals)
%H A370062 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 A370062 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss%E2%80%93Catalan_number">Fuss-Catalan number</a>
%F A370062 T(n,k) = 2*A295260(n,k) - A295224(n,k).
%F A370062 T(n,2*k+1) = A370060(n,2*k+1).
%F A370062 T(n,2*k) = A369929(n,2*k-1).
%e A370062 Array begins:
%e A370062 =============================================
%e A370062 n\k| 3 4 5 6 7 8 9 10 ...
%e A370062 ---+-----------------------------------------
%e A370062 1 | 1 1 1 1 1 1 1 1 ...
%e A370062 2 | 1 1 1 1 1 1 1 1 ...
%e A370062 3 | 1 2 2 3 3 4 4 5 ...
%e A370062 4 | 2 3 4 5 6 7 8 9 ...
%e A370062 5 | 2 7 9 18 21 34 38 55 ...
%e A370062 6 | 5 12 22 35 51 70 92 117 ...
%e A370062 7 | 5 30 52 136 190 368 468 775 ...
%e A370062 8 | 14 55 140 285 506 819 1240 1785 ...
%e A370062 9 | 14 143 340 1155 1950 4495 6545 12350 ...
%e A370062 ...
%o A370062 (PARI) \\ here u is Fuss-Catalan sequence with p = k-1.
%o A370062 u(n, k, r) = {r*binomial((k - 1)*n + r, n)/((k - 1)*n + r)}
%o A370062 T(n, k) = {(if(n%2, u((n-1)/2, k, k\2), if(k%2, u(n/2-1, k, k-1), u(n/2, k, 1))))}
%o A370062 for(n=1, 9, for(k=3, 10, print1(T(n, k), ", ")); print);
%Y A370062 Columns are A208355(n-1), A047749 (k=4), A369472 (k=5), A143546 (k=6), A143547 (k=8), A143554 (k=10), A192893 (k=12).
%Y A370062 Cf. A070914 (rooted), A295224 (oriented), A295260 (unoriented), A369929, A370060 (achiral rooted at cell).
%K A370062 nonn,tabl
%O A370062 1,9
%A A370062 _Andrew Howroyd_, Feb 08 2024