A174740 Triangle read by rows, A027293 * an infinite lower triangular matrix with A147843 as the diagonal and the rest zeros.

1, 1, 2, 2, 2, 0, 3, 4, 0, 0, 5, 6, 0, 0, -5, 7, 10, 0, 0, -5, 0, 11, 14, 0, 0, -10, 0, -7, 15, 22, 0, 0, -15, 0, -7, 0, 22, 30, 0, 0, -25, 0, -14, 0, 0, 30, 44, 0, 0, -35, 0, -21, 0, 0, 0, 42, 60, 0, 0, -55, 0, -35, 0, 0, 0, 0, 56, 84, 0, 0, -75, 0, -49, 0, 0, 0, 0, 12

Offset: 1

Author

Gary W. Adamson, Mar 28 2010

Keywords

• tabl
• sign

Comments

Left border = the partition numbers, A000041; right border = A147843 starting (1, 2, 0, ...).

Row sums apparently give A000203. Check: Sum of row 6 terms = [7, 5, 3, 2, 1, 1] dot [1, 2, 0, 0, -5, 0] = [7 + 10 + 0 + 0 -5 + 0] = 12 = A000203(6).

Examples

			First few rows of the triangle:
   1;
   1,   2;
   2,   2,   0;
   3,   4,   0,   0;
   5,   6,   0,   0,  -5;
   7,  10,   0,   0,  -5,   0;
  11,  14,   0,   0, -10,   0,  -7;
  15,  22,   0,   0, -15,   0,  -7,   0;
  22,  30,   0,   0, -25,   0, -14,   0,   0;
  30,  44,   0,   0, -35,   0, -21,   0,   0,   0;
  42,  60,   0,   0, -55,   0, -35,   0,   0,   0,   0;
  56,  84,   6,   0, -75,   0, -49,   0,   0,   0,   0,  12;
  ...
		

Crossrefs

Cf. A027293, A147843, A000041, A000203.

Formula

Equals triangle A027293 * a lower triangular matrix with A147843 (deleting the first zero) as the right border and the rest zeros.

T(n,k) = A147843(k) * A027293(n,k). - Joerg Arndt, Dec 29 2022

Extensions

Terms corrected by Gary W. Adamson, Dec 27 2022