OFFSET
0,7
FORMULA
The matrix inverse T^-1 equals triangle A101479 (signed).
EXAMPLE
Triangle begins:
1;
1, 1;
-1, 1, 1;
5, -2, 1, 1;
-43, 12, -3, 1, 1;
527, -118, 22, -4, 1, 1;
-8396, 1605, -250, 35, -5, 1, 1;
164672, -27816, 3810, -455, 51, -6, 1, 1;
-3835910, 585046, -72492, 7735, -749, 70, -7, 1, 1;
103464895, -14459138, 1649634, -161336, 14098, -1148, 92, -8, 1, 1; ...
Matrix inverse T^-1 is a signed version of triangle A101479:
1;
-1, 1;
2, -1, 1;
-9, 3, -1, 1;
70, -18, 4, -1, 1;
-795, 170, -30, 5, -1, 1;
11961, -2220, 335, -45, 6, -1, 1; ...
Matrix inverse square T^-2 begins:
1;
-2, 1;
5, -2, 1; <-- row 3 of T
-23, 7, -2, 1;
175, -43, 9, -2, 1; ...
where row 3 of T = row 2 of T^-2 with appended '1'.
Matrix inverse cube T^-3 begins:
1;
-3, 1;
9, -3, 1;
-43, 12, -3, 1; <-- row 4 of T
324, -76, 15, -3, 1; ...
where row 4 of T = row 3 of T^-3 with appended '1'.
Matrix inverse 4th power T^-4 begins:
1;
-4, 1;
14, -4, 1;
-70, 18, -4, 1;
527, -118, 22, -4, 1; <-- row 4 of T
-5624, 1107, -178, 26, -4, 1; ...
where row 5 of T = row 4 of T^-4 with appended '1'.
PROG
(PARI) {T(n, k)=local(A=Mat(1), B); for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, B[i, j]=(A^(-(i-2)))[i-1, j]); )); A=B); return( ((A)[n+1, k+1]))}
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Paul D. Hanna, Aug 25 2007
STATUS
approved