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%I #9 May 31 2013 18:56:44
%S 1,1,1,2,0,1,2,1,0,1,3,1,0,0,1,3,2,1,0,0,1,4,1,1,0,0,0,1,3,3,1,1,0,0,
%T 0,1,6,1,2,1,0,0,0,0,1,5,4,1,1,1,0,0,0,0,1,5,2,2,1,1,0,0,0,0,0,1,6,4,
%U 2,2,1,1,0,0,0,0,0,1,7,2,2,1,1,1,0,0,0,0,0,0,1,7,6,2,2,1,1,1,0,0,0,0,0,0,1
%N Triangle of coefficients for the Inverse Shift-Moebius transform, read by rows.
%C Column k = Inverse-Shift-Moebius transform of all zeros except for a single '1' in position k: [0,0,0,..(k-1)zeros..,1,0,0,0,...].
%C Column 1 is A117171 and equals Inverse-Shift-Moebius([1,0,0,0,...]).
%C Column 2 is A117172 and equals Inverse-Shift-Moebius([0,1,0,0,...]).
%C Column 3 is A117173 and equals Inverse-Shift-Moebius([0,0,1,0,...]).
%C Row sums give A117174 and equals Inverse-Shift-Moebius([1,1,1,...]).
%e Triangle begins:
%e 1;
%e 1, 1;
%e 2, 0, 1;
%e 2, 1, 0, 1;
%e 3, 1, 0, 0, 1;
%e 3, 2, 1, 0, 0, 1;
%e 4, 1, 1, 0, 0, 0, 1;
%e 3, 3, 1, 1, 0, 0, 0, 1;
%e 6, 1, 2, 1, 0, 0, 0, 0, 1;
%e 5, 4, 1, 1, 1, 0, 0, 0, 0, 1;
%e 5, 2, 2, 1, 1, 0, 0, 0, 0, 0, 1;
%e 6, 4, 2, 2, 1, 1, 0, 0, 0, 0, 0, 1;
%e 7, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1;
%e 7, 6, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1;
%e 10, 3, 4, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1;
%e 7, 6, 2, 3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1; ...
%o (PARI) {T(n,k)=if(n<k,0,prod(i=0,n, matrix(n,n,r,c,if(r>=c,if((r+i)%(c+i)==0,1,0))))[n,k])}
%Y Cf. A117171 (column 1), A117172 (column 2), A117173 (column 3), A117174 (row sums), A117165 (inverse), A117162, A008683; A117176.
%K nonn,tabl
%O 1,4
%A _Wouter Meeussen_ and _Paul D. Hanna_, Mar 05 2006
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