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

1,2

Comments

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

Links

Table of n, a(n) for n=1..55.

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) )|.

Example

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.

Sequence in context: A053122 A078812 A104711 * A247239 A198060 A327084

Adjacent sequences: A133109 A133110 A133111 * A133113 A133114 A133115

Keyword

easy,nonn,tabl

Author

Peter Bala, Sep 18 2007

Status

approved