A121439 Matrix inverse of triangle A121334, where A121334(n,k) = C( n*(n+1)/2 + n-k, n-k) for n>=k>=0.

1, -2, 1, -2, -4, 1, -14, 0, -7, 1, -143, -22, 11, -11, 1, -1928, -260, -40, 40, -16, 1, -32219, -3894, -385, -121, 99, -22, 1, -640784, -70644, -6496, -406, -406, 203, -29, 1, -14753528, -1502940, -128723, -9583, 259, -1184, 370, -37, 1, -385500056, -36631962, -2947266, -205620, -14076, 3657, -2967, 621

Offset

0,2

Comments

A triangle having similar properties and complementary construction is the dual triangle A121435.

Links

Table of n, a(n) for n=0..52.

Formula

T(n,k) = [A121412^(-n*(n+1)/2 - 1)](n,k) for n>=k>=0; i.e., row n of A121334^-1 equals row n of matrix power A121412^(-n*(n+1)/2 - 1).

Example

Triangle, A121334^-1, begins:
1;
-2, 1;
-2, -4, 1;
-14, 0, -7, 1;
-143, -22, 11, -11, 1;
-1928, -260, -40, 40, -16, 1;
-32219, -3894, -385, -121, 99, -22, 1;
-640784, -70644, -6496, -406, -406, 203, -29, 1;
-14753528, -1502940, -128723, -9583, 259, -1184, 370, -37, 1; ...
Triangle A121412 begins:
1;
1, 1;
3, 1, 1;
18, 4, 1, 1;
170, 30, 5, 1, 1; ...
Row 3 of A121334^-1 equals row 3 of A121412^(-7), which begins:
1;
-7, 1;
7, -7, 1;
-14, 0, -7, 1; ...
Row 4 of A121334^-1 equals row 4 of A121412^(-11), which begins:
1;
-11, 1;
33, -11, 1;
-22, 22, -11, 1;
-143, -22, 11, -11, 1;...

Prog

(PARI) /* Matrix Inverse of A121334 */ {T(n, k)=local(M=matrix(n+1, n+1, r, c, if(r>=c, binomial(r*(r-1)/2+r-c, r-c)))); return((M^-1)[n+1, k+1])}

Crossrefs

Cf. A121334 (matrix inverse); A121412; variants: A121438, A121440, A121441; A121435 (dual).

Sequence in context: A303084 A302889 A303624 * A307448 A305350 A009205

Adjacent sequences: A121436 A121437 A121438 * A121440 A121441 A121442

Keyword

sign,tabl

Author

Paul D. Hanna, Aug 29 2006

Status

approved