A128046 Triangle read by rows: inverse of the lower triangular matrix (1/1; 1/1, 1/3; 1/1, 1/3, 1/5; ...).

1, -3, 3, 0, -5, 5, 0, 0, -7, 7, 0, 0, 0, -9, 9, 0, 0, 0, 0, -11, 11, 0, 0, 0, 0, 0, -13, 13, 0, 0, 0, 0, 0, 0, -15, 15, 0, 0, 0, 0, 0, 0, 0, -17, 17, 0, 0, 0, 0, 0, 0, 0, 0, -19, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, 23

Offset: 1

Author

Gary W. Adamson, Feb 11 2007

Keywords

• tabl
• sign

Comments

A version of an odd number transform.

Examples

			First few rows of the triangle:
   1;
  -3,  3;
   0, -5,  5;
   0,  0, -7,  7;
  ...
		

Crossrefs

Cf. A126615.

Programs

PARI

tabl(nn) = 1/matrix(nn,nn,i,j,if(i>=j, 1/(2*j-1), 0));
lista(nn) = my(m=tabl(nn)); for (n=1, nn, for (k=1, n, print1(m[n,k], ", "))); \\ Michel Marcus, Feb 08 2023

Formula

Triangle read by rows, replace the right border (1, 2, 3, ...) of A126615 with (1, 3, 5, ...) and the adjacent diagonal (-2, -3, -4, ...) with (-3, -5, -7, ...).

Extensions

Edited by N. J. A. Sloane, Feb 26 2007

More terms from Michel Marcus, Feb 08 2023