%I A127749
%S A127749 1,0,3,0,3,5,0,3,5,7,0,0,0,7,9,0,3,5,0,9,11,0,0,0,0,0,11,13,0,3,5,7,0,
               0,
%T A127749 13,15,0,0,0,0,0,0,0,15,17,0,0,0,7,9,0,0,0,17,19,0,0,0,0,0,0,0,0,0,19,
%U A127749 21,0,3,5
%V A127749 1,0,3,0,-3,5,0,3,-5,7,0,0,0,-7,9,0,-3,5,0,-9,11,0,0,0,0,0,-11,13,0,3,
               -5,7,0,0,-13,15,
%W A127749 0,0,0,0,0,0,0,-15,17,0,0,0,-7,9,0,0,0,-17,19,0,0,0,0,0,0,0,0,0,-19,21,
               0,-3,5
%N A127749 Inverse of number triangle A(n,k)=if(k<=n,if(n<=2k,1/(2n+1),0),0).
%C A127749 Conjectures: row sums modulo 2 are the Fredholm-Rueppel sequence A036987; 
               row sums of triangle modulo 2 are A111982. Row sums are A127750.
%e A127749 Triangle begins
%e A127749 1,
%e A127749 0, 3,
%e A127749 0, -3, 5,
%e A127749 0, 3, -5, 7,
%e A127749 0, 0, 0, -7, 9,
%e A127749 0, -3, 5, 0, -9, 11,
%e A127749 0, 0, 0, 0, 0, -11, 13,
%e A127749 0, 3, -5, 7, 0, 0, -13, 15,
%e A127749 0, 0, 0, 0, 0, 0, 0, -15, 17,
%e A127749 0, 0, 0, -7, 9, 0, 0, 0, -17, 19,
%e A127749 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 21,
%e A127749 0, -3, 5, 0, -9, 11, 0, 0, 0, 0, -21, 23,
%e A127749 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, 25
%e A127749 Inverse of triangle
%e A127749 1,
%e A127749 0, 1/3,
%e A127749 0, 1/5, 1/5,
%e A127749 0, 0, 1/7, 1/7,
%e A127749 0, 0, 1/9, 1/9, 1/9,
%e A127749 0, 0, 0, 1/11, 1/11, 1/11,
%e A127749 0, 0, 0, 1/13, 1/13, 1/13, 1/13,
%e A127749 0, 0, 0, 0, 1/15, 1/15, 1/15, 1/15,
%e A127749 0, 0, 0, 0, 1/17, 1/17, 1/17, 1/17, 1/17,
%e A127749 0, 0, 0, 0, 0, 1/19, 1/19, 1/19, 1/19, 1/19,
%e A127749 0, 0, 0, 0, 0, 1/21, 1/21, 1/21, 1/21, 1/21, 1/21
%Y A127749 Cf. A111967.
%Y A127749 Sequence in context: A073367 A111862 A060858 this_sequence A138188 A014715 
               A131656
%Y A127749 Adjacent sequences: A127746 A127747 A127748 this_sequence A127750 A127751 
               A127752
%K A127749 sign,tabl
%O A127749 0,3
%A A127749 Paul Barry (pbarry(AT)wit.ie), Jan 28 2007