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