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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. 3
 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, 136, 285, 252, 109, 26, 4, 1, 36, 346, 966, 1119, 652, 200, 36, 4, 1, 72, 901, 3188, 4782, 3623, 1502, 352, 50, 5, 1, 136, 2264, 10133, 19116, 18489, 9949, 3120, 570, 65, 5, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 EXAMPLE Triangle begins:    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, 136,  285,  252,  109,   26,   4,  1;   36, 346,  966, 1119,  652,  200,  36,  4, 1;   72, 901, 3188, 4782, 3623, 1502, 352, 50, 5, 1;   ... PROG (PARI) \\ See A303731 for NCPathSetsModDihedral { my(rows=Vec(NCPathSetsModDihedral(vector(10, k, y))-1));   for(n=1, #rows, for(k=1, n, print1(polcoeff(rows[n], k), ", ")); print; ) } CROSSREFS Row sums are A303835. Column 1 is A005418(n-2). Cf. A302828, A303869. Sequence in context: A182457 A334715 A026105 * A060475 A168069 A334014 Adjacent sequences:  A303865 A303866 A303867 * A303869 A303870 A303871 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, May 01 2018 STATUS approved

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Last modified January 25 12:40 EST 2022. Contains 350572 sequences. (Running on oeis4.)