A133112 Triangular array, read by rows, associated with sums of certain Vandermonde determinants.

1, 2, 1, 3, 4, 1, 4, 10, 8, 1, 5, 20, 35, 16, 1, 6, 35, 112, 126, 32, 1, 7, 56, 294, 672, 462, 64, 1, 8, 84, 672, 2772, 4224, 1716, 128, 1, 9, 120, 1386, 9504, 28314, 27456, 6435, 256, 1, 10, 165, 2640, 28314, 151008, 306735, 183040, 24310, 512, 1

Offset: 1

Author

Peter Bala, Sep 18 2007

Keywords

• easy
• nonn
• tabl

Comments

Appears to be the same as A073165 read as a triangular array (excluding the first column).

Examples

			Triangle starts:
  1;
  2 1;
  3 4 1;
  4 10 8 1;
  5 20 35 16 1;
		

Crossrefs

A000292 (column 2), A040977 (column 3), A133111 (column 4). Cf. A103905.

Formula

T(n,k)=1/(1!*2! ... *k!)*Sum_{1 <= x_1, ...,x_k <= n} |det V(x_1, ...,x_k)|, where V(x_1, ...,x_k) is the Vandermonde matrix of order k. For example, T(n,2) = 1/2*Sum_{1<=i,j<= n} |i-j|. T(n,k) = 1/(1!*2! ... *k!)*Sum_{1 <= x_1, ...,x_k <= n} |(Product_{1 <= i < j <= k} (x_j - x_i) )|.