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A303868 Triangle read by rows: T(n,k) = number of noncrossing path sets on n nodes up to rotation and reflection with k paths and isolated vertices allowed.

%I A303868 #8 May 03 2018 14:55:51
%S A303868 1,1,1,1,1,1,2,3,2,1,3,7,6,2,1,6,20,23,11,3,1,10,50,80,51,17,3,1,20,
%T A303868 136,285,252,109,26,4,1,36,346,966,1119,652,200,36,4,1,72,901,3188,
%U A303868 4782,3623,1502,352,50,5,1,136,2264,10133,19116,18489,9949,3120,570,65,5,1
%N A303868 Triangle read by rows: T(n,k) = number of noncrossing path sets on n nodes up to rotation and reflection with k paths and isolated vertices allowed.
%H A303868 Andrew Howroyd, <a href="/A303868/b303868.txt">Table of n, a(n) for n = 1..1275</a>
%e A303868 Triangle begins:
%e A303868    1;
%e A303868    1,   1;
%e A303868    1,   1,    1;
%e A303868    2,   3,    2,    1;
%e A303868    3,   7,    6,    2,    1;
%e A303868    6,  20,   23,   11,    3,    1;
%e A303868   10,  50,   80,   51,   17,    3,   1;
%e A303868   20, 136,  285,  252,  109,   26,   4,  1;
%e A303868   36, 346,  966, 1119,  652,  200,  36,  4, 1;
%e A303868   72, 901, 3188, 4782, 3623, 1502, 352, 50, 5, 1;
%e A303868   ...
%o A303868 (PARI) \\ See A303731 for NCPathSetsModDihedral
%o A303868 { my(rows=Vec(NCPathSetsModDihedral(vector(10, k, y))-1));
%o A303868   for(n=1, #rows, for(k=1, n, print1(polcoeff(rows[n],k), ", ")); print;) }
%Y A303868 Row sums are A303835.
%Y A303868 Column 1 is A005418(n-2).
%Y A303868 Cf. A302828, A303869.
%K A303868 nonn,tabl
%O A303868 1,7
%A A303868 _Andrew Howroyd_, May 01 2018