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%I
%S 1,0,2,0,-2,3,0,2,-3,4,0,0,0,-4,5,0,-2,3,0,-5,6,0,0,0,0,0,-6,7,0,2,-3,
%T 4,0,0,-7,8,0,0,0,0,0,0,0,-8,9,0,0,0,-4,5,0,0,0,-9,10,0,0
%N Inverse of the triangle A(n,k)=if(k<=n,if(n<=2k,1/(n+1),0),0).
%C It is conjectured that all elements of this triangle are integers. It appears that the row sums are the ruler function A001511.
%e Triangle begins
%e 1,
%e 0, 2,
%e 0, -2, 3,
%e 0, 2, -3, 4,
%e 0, 0, 0, -4, 5,
%e 0, -2, 3, 0, -5, 6,
%e 0, 0, 0, 0, 0, -6, 7,
%e 0, 2, -3, 4, 0, 0, -7, 8,
%e 0, 0, 0, 0, 0, 0, 0, -8, 9,
%e 0, 0, 0, -4, 5, 0, 0, 0, -9, 10,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 11,
%e 0, -2, 3, 0, -5, 6, 0, 0, 0, 0, -11, 12,
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 13
%e Triangle is the inverse of the triangle
%e 1,
%e 0, 1/2,
%e 0, 1/3, 1/3,
%e 0, 0, 1/4, 1/4,
%e 0, 0, 1/5, 1/5, 1/5,
%e 0, 0, 0, 1/6, 1/6, 1/6,
%e 0, 0, 0, 1/7, 1/7, 1/7, 1/7,
%e 0, 0, 0, 0, 1/8, 1/8, 1/8, 1/8,
%e 0, 0, 0, 0, 1/9, 1/9, 1/9, 1/9, 1/9,
%e 0, 0, 0, 0, 0, 1/10, 1/10, 1/10, 1/10, 1/10,
%e 0, 0, 0, 0, 0, 1/11, 1/11, 1/11, 1/11, 1/11, 1/11
%K sign,tabl
%O 0,3
%A _Paul Barry_, Jan 24 2007
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