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A293157 Triangle read by rows: T(n,k) = number of linear chord diagrams with n chords such that every chord has length at least k (1 <= k <= n). 9

%I #26 Oct 20 2017 17:20:39

%S 1,3,1,15,5,1,105,36,10,1,945,329,99,20,1,10395,3655,1146,292,40,1,

%T 135135,47844,15422,4317,876,80,1,2027025,721315,237135,69862,16924,

%U 2628,160,1,34459425,12310199,4106680,1251584,332507,67404,7884,320,1,654729075,234615096,79154927,24728326,6944594,1627252,269616,23652,640,1

%N Triangle read by rows: T(n,k) = number of linear chord diagrams with n chords such that every chord has length at least k (1 <= k <= n).

%C There is a surprising change in notation in Sullivan (2016) between Definition 1 and Table 1.

%C The first 11 columns are given in the reference.

%H Everett Sullivan, <a href="https://arxiv.org/abs/1611.02771">Linear chord diagrams with long chords</a>, arXiv preprint arXiv:1611.02771 [math.CO], 2016.

%e Triangle begins:

%e 1;

%e 3, 1;

%e 15, 5, 1;

%e 105, 36, 10, 1;

%e 945, 329, 99, 20, 1;

%e 10395, 3655, 1146, 292, 40, 1;

%e ...

%Y Cf. A000806, A001147, A190823, A190824, A190825, A020714, A278990, A293156, A293881.

%K nonn,tabl

%O 1,2

%A _N. J. A. Sloane_, Oct 10 2017

%E More terms from _Alois P. Heinz_, Oct 17 2017

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Last modified June 7 00:43 EDT 2024. Contains 373140 sequences. (Running on oeis4.)