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%I #16 Oct 18 2018 15:56:31
%S 1,1,0,1,1,0,1,1,1,0,1,1,3,1,0,1,1,3,5,1,0,1,1,3,15,11,1,0,1,1,3,15,
%T 35,21,1,0,1,1,3,15,105,103,43,1,0,1,1,3,15,105,315,343,85,1,0,1,1,3,
%U 15,105,945,1141,979,171,1,0,1,1,3,15,105,945,3465,4779,2915,341,1,0
%N Number A(n,k) of linear chord diagrams having n chords and no chord length larger than k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%C All terms in columns k > 0 are odd.
%H Alois P. Heinz, <a href="/A293960/b293960.txt">Antidiagonals n = 0..40, flattened</a>
%F A(n,k) = Sum_{j=0..k} A293961(n,j).
%F A(n,k) = A(n,n) = A001147(n) for k >= n.
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, 1, 1, 1, ...
%e 0, 1, 1, 1, 1, 1, 1, 1, ...
%e 0, 1, 3, 3, 3, 3, 3, 3, ...
%e 0, 1, 5, 15, 15, 15, 15, 15, ...
%e 0, 1, 11, 35, 105, 105, 105, 105, ...
%e 0, 1, 21, 103, 315, 945, 945, 945, ...
%e 0, 1, 43, 343, 1141, 3465, 10395, 10395, ...
%e 0, 1, 85, 979, 4779, 14857, 45045, 135135, ...
%Y Columns k=0-10 give: A000007, A000012, A001045(n+1), A293995, A293996, A293997, A293998, A293999, A294000, A294001, A294002.
%Y Main diagonal gives A001147.
%Y Cf. A293961.
%K nonn,tabl
%O 0,13
%A _Alois P. Heinz_, Oct 20 2017
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