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%I #12 May 03 2018 17:04:25
%S 1,1,2,3,8,19,64,212,833,3360,14476,63848,289892,1338000,6275589,
%T 29791100,142973014,692507861,3382070233,16638445745,82395500651,
%U 410463736691,2055858519575,10347925039015,52321093290715,265648012207312,1353953547877556,6925400869302520
%N Number of noncrossing path sets on n nodes up to rotation and reflection with isolated vertices allowed.
%H Andrew Howroyd, <a href="/A303835/b303835.txt">Table of n, a(n) for n = 0..200</a>
%e Case n=3: There are 3 possibilities:
%e .
%e o o o
%e / \
%e o o o---o o o
%e .
%e Case n=4: There are 8 possibilities:
%e .
%e o o o o o o o o o o o---o o o o---o
%e / | / | | /
%e o o o---o o o o---o o---o o---o o---o o---o
%e .
%o (PARI) \\ See A303731 for NCPathSetsModDihedral
%o Vec(NCPathSetsModDihedral(vector(30, k, 1)))
%Y Cf. A303731, A303839.
%K nonn
%O 0,3
%A _Andrew Howroyd_, May 01 2018
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