A121441 Matrix inverse of triangle A121336, where A121336(n,k) = C( n*(n+1)/2 + n-k + 2, n-k) for n>=k>=0.

1, -4, 1, 3, -6, 1, -12, 9, -9, 1, -117, -26, 26, -13, 1, -1656, -216, -69, 63, -18, 1, -28506, -3396, -294, -212, 132, -24, 1, -578274, -63116, -5766, -124, -620, 248, -31, 1, -13504179, -1365546, -116116, -8892, 1170, -1612, 429, -39, 1, -356633784, -33696726, -2696316, -186860, -15000, 6228, -3736

Offset: 0

Author

Paul D. Hanna, Aug 29 2006

Keywords

• sign
• tabl

Comments

A triangle having similar properties and complementary construction is the dual triangle A121437.

Examples

			Triangle, A121336^-1, begins:
1;
-4, 1;
3, -6, 1;
-12, 9, -9, 1;
-117, -26, 26, -13, 1;
-1656, -216, -69, 63, -18, 1;
-28506, -3396, -294, -212, 132, -24, 1;
-578274, -63116, -5766, -124, -620, 248, -31, 1;
-13504179, -1365546, -116116, -8892, 1170, -1612, 429, -39, 1; ...
Triangle A121412 begins:
1;
1, 1;
3, 1, 1;
18, 4, 1, 1;
170, 30, 5, 1, 1; ...
Row 3 of A121336^-1 equals row 3 of A121412^(-9), which begins:
1;
-9, 1;
18, -9, 1;
-12, 9, -9, 1; ...
Row 4 of A121336^-1 equals row 4 of A121412^(-13), which begins:
1;
-13, 1;
52, -13, 1;
-52, 39, -13, 1;
-117, -26, 26, -13, 1; ...
		

Crossrefs

Cf. A121336 (matrix inverse); A121412; variants: A121438, A121439, A121440; A121437 (dual).

Programs

PARI

/* Matrix Inverse of A121336 */ {T(n,k)=local(M=matrix(n+1,n+1,r,c,if(r>=c,binomial(r*(r-1)/2+r-c+2,r-c)))); return((M^-1)[n+1,k+1])}

Formula

T(n,k) = [A121412^(-n*(n+1)/2 - 3)](n,k) for n>=k>=0; i.e., row n of A121336^-1 equals row n of matrix power A121412^(-n*(n+1)/2 - 3).