%I A117162
%S A117162 1,1,1,1,1,1,0,2,1,1,1,0,2,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,0,0,2,2,1,2,1,
%T A117162 1,0,1,1,2,2,1,2,1,1,1,1,3,0,1,2,1,2,1,1,1,1,1,3,0,1,2,1,2,1,1,0,2,2,0,
%U A117162 4,1,1,2,1,2,1,1,1,0,2,2,0,4,1,1,2,1,2,1,1
%V A117162 1,-1,1,-1,-1,1,0,-2,-1,1,-1,0,-2,-1,1,1,-1,-1,-2,-1,1,-1,1,-1,-1,-2,-1,
               1,0,0,2,-2,-1,
%W A117162 -2,-1,1,0,1,-1,2,-2,-1,-2,-1,1,1,-1,3,0,1,-2,-1,-2,-1,1,-1,1,-1,3,0,1,
               -2,-1,-2,-1,1,0,
%X A117162 2,2,0,4,-1,1,-2,-1,-2,-1,1,-1,0,2,2,0,4,-1,1,-2,-1,-2,-1,1
%N A117162 Matrix inverse of triangle A112682.
%C A117162 The limit of the columns (without leading zeros) is A117166,
%C A117162 the Shift-Moebius transform of [1,0,0,0,...] (cf. A117165).
%F A117162 Column k+1 equals the Moebius transform of column k preceded by a zero,
%F A117162 where column k includes the k-1 zeros above the diagonal, for k>=1,
%F A117162 starting with A008683 in column 1.
%e A117162 Column 1 equals A008683 = Moebius transform of [1,0,0,0,...].
%e A117162 Column 2 = Moebius transform of column 1 preceded by a zero:
%e A117162 [0,1,-1,-2,0,-1,1,0,...] = Moebius([0,
%e A117162 1,-1,-1,0,-1,1,-1,...]).
%e A117162 Column 3 = Moebius transform of column 2 preceded by a zero:
%e A117162 [0,0,1,-1,-2,-1,-1,2,...] = Moebius([0,
%e A117162 0,1,-1,-2,0,-1,1,...]).
%e A117162 Column 4 = Moebius transform of column 3 preceded by a zero:
%e A117162 [0,0,0,1,-1,-2,-1,-2,...] = Moebius([0,
%e A117162 0,0,1,-1,-2,-1,-1,...]).
%e A117162 Triangle begins:
%e A117162 1;
%e A117162 -1, 1;
%e A117162 -1,-1, 1;
%e A117162 0,-2,-1, 1;
%e A117162 -1, 0,-2,-1, 1;
%e A117162 1,-1,-1,-2,-1, 1;
%e A117162 -1, 1,-1,-1,-2,-1, 1;
%e A117162 0, 0, 2,-2,-1,-2,-1, 1;
%e A117162 0, 1,-1, 2,-2,-1,-2,-1, 1;
%e A117162 1,-1, 3, 0, 1,-2,-1,-2,-1, 1;
%e A117162 -1, 1,-1, 3, 0, 1,-2,-1,-2,-1, 1;
%e A117162 0, 2, 2, 0, 4,-1, 1,-2,-1,-2,-1, 1;
%e A117162 -1, 0, 2, 2, 0, 4,-1, 1,-2,-1,-2,-1, 1; ...
%Y A117162 Cf. A112682 (inverse), A008683 (column 1), A117163 (column 2), A117164 
               (column 3); A117165 (Shift-Moebius), A117170 (inverse Shift-Moebius).
%Y A117162 Sequence in context: A135997 A026609 A090340 this_sequence A146061 A135936 
               A109707
%Y A117162 Adjacent sequences: A117159 A117160 A117161 this_sequence A117163 A117164 
               A117165
%K A117162 sign,tabl
%O A117162 1,8
%A A117162 Wouter Meeussen (wouter.meeussen(AT)pandora.be) and Paul D. Hanna (pauldhanna(AT)juno.com), 
               Mar 05 2006