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 A295222 #17 Dec 29 2017 10:31:47
%S A295222 1,1,1,1,1,3,1,1,5,10,1,1,6,22,30,1,1,8,40,116,99,1,1,9,64,285,612,
%T A295222 335,1,1,11,92,578,2126,3399,1144,1,1,12,126,1015,5481,16380,19228,
%U A295222 3978,1,1,14,166,1641,11781,54132,129456,111041,14000
%N A295222 Array read by antidiagonals: T(n,k) is the number of nonequivalent dissections of a polygon into n k-gons by nonintersecting diagonals rooted at a cell up to rotation (k >= 3).
%C A295222 The polygon prior to dissection will have n*(k-2)+2 sides.
%C A295222 In the Harary, Palmer and Read reference these are the sequences called F.
%H A295222 Andrew Howroyd, <a href="/A295222/b295222.txt">Table of n, a(n) for n = 1..1275</a>
%H A295222 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 A295222 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss%E2%80%93Catalan_number">Fuss-Catalan number</a>
%F A295222 T(n,k) = Sum_{d|gcd(n-1,k)} phi(d)*u((n-1)/d, k, k/d)/k where u(n,k,r) = r*binomial((k - 1)*n + r, n)/((k - 1)*n + r).
%F A295222 T(n,k) ~ n*A070914(n,k-2)/(n*(k-2)+2) for fixed k.
%e A295222 Array begins:
%e A295222 ===========================================================
%e A295222 n\k| 3 4 5 6 7 8
%e A295222 ---|-------------------------------------------------------
%e A295222 1 | 1 1 1 1 1 1 ...
%e A295222 2 | 1 1 1 1 1 1 ...
%e A295222 3 | 3 5 6 8 9 11 ...
%e A295222 4 | 10 22 40 64 92 126 ...
%e A295222 5 | 30 116 285 578 1015 1641 ...
%e A295222 6 | 99 612 2126 5481 11781 22386 ...
%e A295222 7 | 335 3399 16380 54132 141778 317860 ...
%e A295222 8 | 1144 19228 129456 548340 1753074 4638348 ...
%e A295222 9 | 3978 111041 1043460 5672645 22137570 69159400 ...
%e A295222 10 | 14000 650325 8544965 59653210 284291205 1048927880 ...
%e A295222 ...
%t A295222 u[n_, k_, r_] := r*Binomial[(k - 1)*n + r, n]/((k - 1)*n + r);
%t A295222 T[n_, k_] := DivisorSum[GCD[n-1, k], EulerPhi[#]*u[(n-1)/#, k, k/#]&]/k;
%t A295222 Table[T[n - k + 3, k], {n, 1, 10}, {k, n + 2, 3, -1}] // Flatten (* _Jean-François Alcover_, Nov 21 2017, after _Andrew Howroyd_ *)
%o A295222 (PARI) \\ here u is Fuss-Catalan sequence with p = k+1.
%o A295222 u(n,k,r)={r*binomial((k - 1)*n + r, n)/((k - 1)*n + r)}
%o A295222 T(n,k)=sumdiv(gcd(n-1,k), d, eulerphi(d)*u((n-1)/d, k, k/d))/k;
%o A295222 for(n=1, 10, for(k=3, 8, print1(T(n, k), ", ")); print);
%o A295222 (Python)
%o A295222 from sympy import binomial, gcd, totient, divisors
%o A295222 def u(n, k, r): return r*binomial((k - 1)*n + r, n)//((k - 1)*n + r)
%o A295222 def T(n, k): return sum([totient(d)*u((n - 1)//d, k, k//d) for d in divisors(gcd(n - 1, k))])//k
%o A295222 for n in range(1, 11): print([T(n, k) for k in range(3, 9)]) # _Indranil Ghosh_, Dec 13 2017, after PARI
%Y A295222 Columns k=3..5 are A003441, A005033, A005037.
%Y A295222 Cf. A033282, A070914, A295224, A295259, A295260.
%K A295222 nonn,tabl
%O A295222 1,6
%A A295222 _Andrew Howroyd_, Nov 17 2017