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%I #5 Sep 29 2018 18:45:43
%S 1,0,1,0,-1,2,0,1,-2,6,0,0,0,-6,24,0,-1,2,0,-24,120,0,0,0,0,0,-120,
%T 720,0,1,-2,6,0,0,-720,5040,0,0,0,0,0,0,0,-5040,40320,0,0,0,-6,24,0,0,
%U 0,-40320,362880,0,0,0,0,0,0,0,0,0
%N Inverse of number triangle A(n,k) = 1/n! if k <= n <= 2k, 0 otherwise.
%C It is conjectured that this is an integer triangle. Row sums are A127756.
%e Triangle begins
%e 1;
%e 0, 1;
%e 0, -1, 2;
%e 0, 1, -2, 6;
%e 0, 0, 0, -6, 24;
%e 0, -1, 2, 0, -24, 120;
%e 0, 0, 0, 0, 0, -120, 720;
%e 0, 1, -2, 6, 0, 0, -720, 5040;
%e 0, 0, 0, 0, 0, 0, 0, -5040, 40320;
%e 0, 0, 0, -6, 24, 0, 0, 0, -40320, 362880;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, -362880, 3628800;
%e 0, -1, 2, 0, -24, 120, 0, 0, 0, 0, -3628800, 39916800;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -39916800, 479001600;
%e Inverse of triangle begins
%e 1;
%e 0, 1;
%e 0, 1/2, 1/2;
%e 0, 0, 1/6, 1/6;
%e 0, 0, 1/24, 1/24, 1/24;
%e 0, 0, 0, 1/120, 1/120, 1/120;
%e 0, 0, 0, 1/720, 1/720, 1/720, 1/720;
%e 0, 0, 0, 0, 1/5040, 1/5040, 1/5040, 1/5040;
%e 0, 0, 0, 0, 1/40320, 1/40320, 1/40320, 1/40320, 1/40320;
%e 0, 0, 0, 0, 0, 1/362880, 1/362880, 1/362880, 1/362880, 1/362880;
%e 0, 0, 0, 0, 0, 1/3628800, 1/3628800, 1/3628800, 1/3628800, 1/3628800, 1/3628800;
%K sign,tabl
%O 0,6
%A _Paul Barry_, Jan 28 2007
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