A105619 Matrix inverse of triangle A105615.

1, -2, 1, -2, -4, 1, -10, -2, -6, 1, -74, -10, -2, -8, 1, -706, -74, -10, -2, -10, 1, -8162, -706, -74, -10, -2, -12, 1, -110410, -8162, -706, -74, -10, -2, -14, 1, -1708394, -110410, -8162, -706, -74, -10, -2, -16, 1, -29752066, -1708394, -110410, -8162, -706, -74, -10, -2, -18, 1

Offset: 0

Author

Paul D. Hanna, Apr 16 2005

Keywords

• sign
• tabl

Comments

Except for the initial few terms, all columns are equal to negative A000698 (related to double factorials).

Examples

			Triangle begins:
1;
-2,1;
-2,-4,1;
-10,-2,-6,1;
-74,-10,-2,-8,1;
-706,-74,-10,-2,-10,1;
-8162,-706,-74,-10,-2,-12,1;
-110410,-8162,-706,-74,-10,-2,-14,1;
-1708394,-110410,-8162,-706,-74,-10,-2,-16,1; ...
		

Crossrefs

Cf. A105615, A000698, A105620 (matrix square-root).

Programs

PARI

T(n,k)=if(n=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))[n+1,k+1])