%N Number of dissections of a 2n-gon into polygons with even number of sides counted up to rotations and reflections.
%H Andrew Howroyd, <a href="/A290722/b290722.txt">Table of n, a(n) for n = 2..200</a>
%H Evgeniy Krasko, Alexander Omelchenko, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p17">Brown's Theorem and its Application for Enumeration of Dissections and Planar Trees</a>, The Electronic Journal of Combinatorics, 22 (2015), #P1.17.
%e For a(4) = 4 the dissections of an octagon are: two dissections into 3 quadrangles; a dissection into one hexagon and one quadrangle; a dissection into one octagon.
%o (PARI) \\ See A295419 for DissectionsModDihedral().
%o select(v->v>0, DissectionsModDihedral(apply(v->v%2==0, [1..50]))) \\ _Andrew Howroyd_, Nov 22 2017
%Y Cf. A003168 (counted distinctly).
%Y Cf. A001004, A290816, A295419.
%A _Evgeniy Krasko_, Sep 03 2017
%E Terms a(8) and beyond from _Andrew Howroyd_, Nov 22 2017