A209155 Triangle read by rows: numerators of Stirling-like triangle of rational numbers.

-1, -1, 1, -1, 3, -1, -1, 1, -2, 1, -1, 5, -5, 5, -1, -1, 1, -5, 5, -3, 1, -1, 7, -7, 35, -7, 7, -1, -1, 4, -28, 7, -14, 14, -4, 1

Offset: 1

Author

N. J. A. Sloane, Mar 05 2012

Keywords

• sign
• frac
• tabl
• more

Comments

In Joseph M. Santmyer's paper, Table 1 (A209155/A209156) seems to be incorrect. The paper presents the formula c(n,r) = -(n/(r+1)) * (D(n-1,r-1)/D(n,r)) * c(n-1,r-1) for 1 < r < n-1, where D(n,r) = A323855(n,r). However, in Table 1, the value of c(5,2) is given as -5/3, which does not match the result obtained by applying the formula: -5/3 * D(4,1)/D(5,2) * c(4,1) equals -5. - Jinyuan Wang, Mar 17 2025

Examples

			Triangle begins:
  -1;
  -1,  1;
  -1, 3/2,    -1;
  -1,   1,    -2,    1;
  -1,   5,  -5/3,  5/2,   -1;
  -1,   1,    -5,  5/2,   -3,    1;
  -1,   7,  -7/3, 35/4, -7/2,  7/2, -1;
  -1,   4, -28/3,  7/3,  -14, 14/3, -4, 1;
  ...
		

Links

• Joseph M. Santmyer, A Stirling like sequence of rational numbers, Discrete Math. 171 (1997), no. 1-3, 229-235. MR1454453.

Crossrefs

Cf. A209156, A323855.