A107726 Matrix inverse of triangle A107717, read by rows.

1, -3, 1, -3, -6, 1, -21, -3, -9, 1, -219, -21, -3, -12, 1, -2973, -219, -21, -3, -15, 1, -49323, -2973, -219, -21, -3, -18, 1, -964173, -49323, -2973, -219, -21, -3, -21, 1, -21680571, -964173, -49323, -2973, -219, -21, -3, -24, 1, -551173053, -21680571, -964173, -49323, -2973, -219, -21, -3, -27, 1

Offset: 0

Author

Paul D. Hanna, May 30 2005

Keywords

• sign
• tabl

Comments

Except for initial terms, each column is the same and equals negative A107716 (inverse INVERT of triple factorials).

Examples

			Triangle begins:
1;
-3,1;
-3,-6,1;
-21,-3,-9,1;
-219,-21,-3,-12,1;
-2973,-219,-21,-3,-15,1;
-49323,-2973,-219,-21,-3,-18,1;
-964173,-49323,-2973,-219,-21,-3,-21,1; ...
Matrix inverse is A107717:
1;
3,1;
21,6,1;
219,57,9,1;
2973,723,111,12,1;
49323,11361,1713,183,15,1; ...
		

Crossrefs

Cf. A107716, A107717.

Programs

PARI

T(n,k)=if(n=j,if(m==j,1,if(m==j+1,-3*j, polcoeff(1/sum(i=0,m-j,prod(r=0,i-1,3*r+1)*x^i)+O(x^m),m-j)))))[n+1,k+1])