A105620 Matrix inverse square-root of triangle A105615.

1, -1, 1, -2, -2, 1, -10, -4, -3, 1, -74, -20, -7, -4, 1, -706, -148, -39, -11, -5, 1, -8162, -1412, -315, -70, -16, -6, 1, -110410, -16324, -3243, -635, -116, -22, -7, 1, -1708394, -220820, -40167, -7264, -1183, -180, -29, -8, 1, -29752066, -3416788, -579159, -99191, -15065, -2049, -265, -37, -9, 1

Offset: 0

Author

Paul D. Hanna, Apr 16 2005

Keywords

• sign
• tabl

Comments

Column 0 is negative A000698 (related to double factorials). Column 1 equals twice column 0 after the initial term.

Examples

			Triangle begins:
1;
-1,1;
-2,-2,1;
-10,-4,-3,1;
-74,-20,-7,-4,1;
-706,-148,-39,-11,-5,1;
-8162,-1412,-315,-70,-16,-6,1;
-110410,-16324,-3243,-635,-116,-22,-7,1;
-1708394,-220820,-40167,-7264,-1183,-180,-29,-8,1;
-29752066,-3416788,-579159,-99191,-15065,-2049,-265,-37,-9,1; ...
		

Crossrefs

Cf. A105615, A105619 (matrix square), A105623 (matrix inverse), A000698 (column 0), A105621 (column 2), A105622 (row sums).

Programs

PARI

T(n,k)=local(R,M=matrix(n+1,n+1,m,j,if(m>=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)))))); R=(M+M^0)/2;for(i=1,floor(2*log(n+2)),R=(R+M*R^(-1))/2); return(if(n