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%I #6 Sep 30 2018 02:35:36
%S 1,0,2,0,-2,2,0,2,-2,2,0,0,0,-2,2,0,-2,2,0,-2,2,0,0,0,0,0,-2,2,0,2,-2,
%T 2,0,0,-2,2,0,0,0,0,0,0,0,-2,2,0,0,0,-2,2,0,0,0,-2,2,0,0,0,0,0,0,0,0,
%U 0,-2,2,0,-2,2,0,-2,2,0,0,0,0,-2,2
%N Inverse of number triangle A(n,k) = 1/(2 - 0^n), if k <= n <= 2k, 0 otherwise.
%C Row sums are A069517 (conjecture).
%e Triangle begins
%e 1;
%e 0, 2;
%e 0, -2, 2;
%e 0, 2, -2, 2;
%e 0, 0, 0, -2, 2;
%e 0, -2, 2, 0, -2, 2;
%e 0, 0, 0, 0, 0, -2, 2;
%e 0, 2, -2, 2, 0, 0, -2, 2;
%e 0, 0, 0, 0, 0, 0, 0, -2, 2;
%e 0, 0, 0, -2, 2, 0, 0, 0, -2, 2;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2;
%e 0, -2, 2, 0, -2, 2, 0, 0, 0, 0, -2, 2;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2;
%e Inverse of triangle begins
%e 1;
%e 0, 1/2;
%e 0, 1/2, 1/2;
%e 0, 0, 1/2, 1/2;
%e 0, 0, 1/2, 1/2, 1/2;
%e 0, 0, 0, 1/2, 1/2, 1/2;
%e 0, 0, 0, 1/2, 1/2, 1/2, 1/2;
%e 0, 0, 0, 0, 1/2, 1/2, 1/2, 1/2;
%e 0, 0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1/2;
%e 0, 0, 0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1/2;
%e 0, 0, 0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2;
%K sign,tabl
%O 0,3
%A _Paul Barry_, Jan 29 2007