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

0,4

Comments

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

Links

Table of n, a(n) for n=0..54.

Example

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; ...

Prog

(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<k || k<0, 0, R[n+1, k+1]))

Crossrefs

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

Sequence in context: A285068 A306149 A134896 * A182002 A184251 A262348

Adjacent sequences: A105617 A105618 A105619 * A105621 A105622 A105623

Keyword

sign,tabl

Author

Paul D. Hanna, Apr 16 2005

Status

approved