Search: id:A067310
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%I A067310
%S A067310 1,0,1,0,0,2,0,0,1,5,0,0,0,6,14,0,0,0,3,28,42,0,0,0,1,28,120,132,0,0,0,
%T A067310 0,20,180,495,429,0,0,0,0,10,195,990,2002,1430,0,0,0,0,4,165,1430,5005,
%U A067310 8008,4862,0,0,0,0,1,117,1650,9009,24024,31824,16796,0,0,0,0,0,70,1617
%N A067310 Square table read by antidiagonals of number of ways of arranging n chords 
               on a circle with k simple intersections (i.e. no intersections with 
               3 or more chords).
%H A067310 H. Bottomley, <a href="a002694.gif">Illustration for A000108, A001147, 
               A002694, A067310 and A067311</a>
%H A067310 <a href="http://groups.google.com/groups?threadm=3c40c437.108548986%40news.btinternet.com&rnum=1">
               alt.math.recreational discussion</a>
%F A067310 Sum_{0<=j<n} (-1)^j * C((n-j)*(n-j+1)/2-1-i, n-1) * (C(2n, j)-C(2n, j-1))
%e A067310 Rows start: 1,0,0,0,0,0,0,...; 1,0,0,0,0,0,0,...; 2,1,0,0,0,0,0,...; 
               5,6,3,1,0,0,0,...; 14,28,28,20,10,4,1,...; etc., i.e. there are 5 
               ways of arranging 3 chords with no intersections, 6 with one, 3 with 
               two and 1 with three.
%Y A067310 Row sums are A001147 (Double factorial). Columns include A000108 (Catalan) 
               for k=0 and A002694 for k=1. A067311 has a different view of the 
               same table.
%Y A067310 Sequence in context: A109077 A137585 A072458 this_sequence A122890 A138497 
               A113129
%Y A067310 Adjacent sequences: A067307 A067308 A067309 this_sequence A067311 A067312 
               A067313
%K A067310 nonn,tabl
%O A067310 0,6
%A A067310 Henry Bottomley (se16(AT)btinternet.com), Jan 14 2002

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