0,7

The matrix inverse T^-1 equals triangle A101479 (signed).

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 4-th 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'.

(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]))}

Cf. A101479; columns: A132691, A132692, A132693, A132694.

Sequence in context: A010128 A029764 A136301 this_sequence A089086 A038631 A133615

Adjacent sequences: A132687 A132688 A132689 this_sequence A132691 A132692 A132693

tabl,sign

Paul D. Hanna (pauldhanna(AT)juno.com), Aug 25 2007