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A133112 Triangular array, read by rows, associated with sums of certain Vandermonde determinants. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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 A159856

Adjacent sequences:  A133109 A133110 A133111 * A133113 A133114 A133115

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Bala, Sep 18 2007

STATUS

approved

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Last modified July 21 20:57 EDT 2017. Contains 289648 sequences.