OFFSET
1,4
COMMENTS
Column k = Shift-Moebius transform of a sequence of all zeros except for a single '1' in position k: [0,0,0,..(k-1)zeros..,1,0,0,0,...].
Column 1 is A117166, the Shift-Moebius transform of [1,0,0,0,...].
Column 2 is A117167, the Shift-Moebius transform of [0,1,0,0,...].
Column 3 is A117168, the Shift-Moebius transform of [0,0,1,0,...].
Row sums give A117169, the Shift-Moebius transform of [1,1,1,...].
FORMULA
The Shift-Moebius transform of a sequence B is equal to the limit of the iteration: let C_1 = B and for k>1, C_{k+1} = Moebius transform of C_k preceded by k zeros, then shift left k places (to drop the leading k zeros).
EXAMPLE
Triangle begins:
1;
-1, 1;
-2, 0, 1;
-1,-1, 0, 1;
-2,-1, 0, 0, 1;
1,-2,-1, 0, 0, 1;
-1,-1,-1, 0, 0, 0, 1;
3,-2,-1,-1, 0, 0, 0, 1;
0, 0,-2,-1, 0, 0, 0, 0, 1;
4,-2,-1,-1,-1, 0, 0, 0, 0, 1;
4, 0,-2,-1,-1, 0, 0, 0, 0, 0, 1;
5, 1,-1,-2,-1,-1, 0, 0, 0, 0, 0, 1;
1, 2,-1,-1,-1,-1, 0, 0, 0, 0, 0, 0, 1;
7, 0, 0,-2,-1,-1,-1, 0, 0, 0, 0, 0, 0, 1;
6, 3,-2,-1,-2,-1,-1, 0, 0, 0, 0, 0, 0, 0, 1;
5, 3, 1,-2,-1,-1,-1,-1, 0, 0, 0, 0, 0, 0, 0, 1; ...
PROG
(PARI) {T(n, k)=if(n<k, 0, prod(i=0, n, matrix(n, n, r, c, if(r>=c, if((r+n-i)%(c+n-i)==0, moebius((r+n-i)/(c+n-i)), 0))))[ n, k])}
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Wouter Meeussen and Paul D. Hanna, Mar 05 2006
STATUS
approved