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

0,2

Comments

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

Links

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

Example

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; ...

Prog

(PARI) T(n, k)=if(n<k || k<0, 0, 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)))))[n+1, k+1])

Crossrefs

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

Sequence in context: A119765 A303325 A077901 * A302212 A302460 A303242

Adjacent sequences: A105616 A105617 A105618 * A105620 A105621 A105622

Keyword

sign,tabl

Author

Paul D. Hanna, Apr 16 2005

Status

approved