%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