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%I #5 Sep 29 2018 18:44:54
%S 1,0,3,0,-3,4,0,3,-4,7,0,0,0,-7,11,0,-3,4,0,-11,18,0,0,0,0,0,-18,29,0,
%T 3,-4,7,0,0,-29,47,0,0,0,0,0,0,0,-47,76,0,0,0,-7,11,0,0,0,-76,123,0,0,
%U 0,0,0,0,0,0,0,-123,199,0,-3,4,0,-11,18,0,0
%N Inverse of number triangle A(n,k) = 1/L(n+1) if k <= n <= 2k, 0 otherwise, where L(n) = A000032(n).
%C Row sums are A127754.
%e Triangle begins
%e 1;
%e 0, 3;
%e 0, -3, 4;
%e 0, 3, -4, 7;
%e 0, 0, 0, -7, 11;
%e 0, -3, 4, 0, -11, 18;
%e 0, 0, 0, 0, 0, -18, 29;
%e 0, 3, -4, 7, 0, 0, -29, 47;
%e 0, 0, 0, 0, 0, 0, 0, -47, 76;
%e 0, 0, 0, -7, 11, 0, 0, 0, -76, 123;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, -123, 199;
%e 0, -3, 4, 0, -11, 18, 0, 0, 0, 0, -199, 322;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -322, 521;
%e Inverse of triangle begins
%e 1;
%e 0, 1/3;
%e 0, 1/4, 1/4;
%e 0, 0, 1/7, 1/7;
%e 0, 0, 1/11, 1/11, 1/11;
%e 0, 0, 0, 1/18, 1/18, 1/18;
%e 0, 0, 0, 1/29, 1/29, 1/29, 1/29;
%e 0, 0, 0, 0, 1/47, 1/47, 1/47, 1/47;
%e 0, 0, 0, 0, 1/76, 1/76, 1/76, 1/76, 1/76;
%e 0, 0, 0, 0, 0, 1/123, 1/123, 1/123, 1/123, 1/123;
%e 0, 0, 0, 0, 0, 1/199, 1/199, 1/199, 1/199, 1/199, 1/199;
%Y Cf. A127711.
%K sign,tabl
%O 0,3
%A _Paul Barry_, Jan 28 2007