A144032 Triangle read by rows: T(n,k) = A002321(n-k+1)*A144031(k-1).

1, 0, 1, -1, 0, 1, -1, -1, 0, 0, -2, -1, -1, 0, -2, -1, -2, -1, 0, 0, -6, -2, -1, -2, 0, 2, 0, -10, -2, -2, -1, 0, 2, 6, 0, -13, -2, -2, -2, 0, 46, 10, 0, -10, -1, -2, -2, 0, 2, 12, 10, 13, 0, 4, -2, -1, -2, 0, 4, 6, 10, 13, 10, 0, 36, -2, -2, -1, 0, 4, 12, 10, 26, 10, -4, 0, 84, -3

Offset: 1

Author

Gary W. Adamson, Sep 07 2008

Keywords

• tabl
• sign

Comments

Row sums = A144031, the INVERT transform of A002321.

Left border = the Mertens's function, A002321.

Right border = A144031 shifted.

Sum of n-th row terms = rightmost term of (n+1)-th row.

Examples

			First few rows of the triangle:
   1;
   0,  1;
  -1,  0,  1;
  -1, -1,  0, 0;
  -2, -1, -1, 0, -2;
  -1, -2, -1, 0,  0, -6;
  -2, -1, -2, 0,  2,  0, -10;
  -2, -2, -1, 0,  2,  6,   0, -13;
  -2, -2, -2, 0,  4,  6,  10,   0, -10;
  ...
Row 5 = (-2, -1, -1, 0, -2) termwise products of (-2, -1, -1, 0, 1) and (1, 1, 1, 0, -2); = ((-2)*(1), (-1)*(1), (-1)*(1), (0)*(0), (1)*(-2)). (-2, -1, -1, 0, 1) = the first 5 terms of A002321, the Mertens's function. (1, 1, 1, 0, -2) = 5 shifted terms of A144031.
		

Crossrefs

Cf. A002321, A144031.