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 A003454 M1676 #37 Mar 22 2022 02:26:08
%S A003454 1,2,6,25,107,509,2468,12258,61797,315830,1630770,8498303,44629855,
%T A003454 235974495,1255105304,6710883952,36050676617,194478962422,
%U A003454 1053120661726,5722375202661,31191334491891,170504130213135,934495666529380,5134182220623958,28270742653671621
%N A003454 Number of nonequivalent dissections of an n-gon by nonintersecting diagonals rooted at a cell up to rotation.
%C A003454 Total number of dissections of an n-gon into polygons without reflection and rooted at a cell. - _Sean A. Irvine_, May 14 2015
%C A003454 Say two n-gons are equivalent (or in the same convexity class) if there is a bijection between the edges and vertices which preserves inclusion of vertices and edges, preserves the handedness of the polygon (does not reflect the polygon over a line), maps vertices of the convex hulls to each other, and induces an equivalence on each nontrivially connected component of Hull(X) \ X. This sequence is the number of convexity classes for an n-gon, up to rotation. - _Griffin N. Macris_, Mar 02 2021
%D A003454 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003454 Andrew Howroyd, <a href="/A003454/b003454.txt">Table of n, a(n) for n = 3..200</a>
%H A003454 P. Lisonek, <a href="http://dx.doi.org/10.1006/jsco.1995.1066">Closed forms for the number of polygon dissections</a>, Journal of Symbolic Computation 20 (1995), 595-601.
%H A003454 Ronald C. Read, <a href="http://dx.doi.org/10.1007/BF03031688">On general dissections of a polygon</a>, Aequat. math. 18 (1978) 370-388.
%F A003454 G.f.: -f(x) - (f(x)^2 + f(x^2))/2 + Sum_{k>=1} (phi(k)/k)*log(1/(1 - f(x^k))), where phi(k) is Euler's Totient function and f(x) = (1 + x - sqrt(1 - 6x + x^2))/4 is related to the o.g.f. for A001003. - _Griffin N. Macris_, Mar 02 2021
%o A003454 (PARI) \\ See A003442 for DissectionsModCyclicRooted.
%o A003454 DissectionsModCyclicRooted(apply(i->1, [1..30])) \\ _Andrew Howroyd_, Nov 22 2017
%Y A003454 Cf. A001004, A003455, A003456, A005033, A295222.
%Y A003454 Cf. A003442.
%K A003454 nonn
%O A003454 3,2
%A A003454 _N. J. A. Sloane_
%E A003454 More terms from _Sean A. Irvine_, May 14 2015
%E A003454 Name clarified by _Andrew Howroyd_, Nov 22 2017