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%I #2 Mar 31 2012 13:47:33
%S 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,
%T 64,1,8,84,672,2772,4224,1716,128,1,9,120,1386,9504,28314,27456,6435,
%U 256,1,10,165,2640,28314,151008,306735,183040,24310,512,1
%N Triangular array, read by rows, associated with sums of certain Vandermonde determinants.
%C Appears to be the same as A073165 read as a triangular array (excluding the first column).
%F 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) )|.
%e Triangle starts
%e 1;
%e 2 1;
%e 3 4 1;
%e 4 10 8 1;
%e 5 20 35 16 1;
%Y A000292 (column 2), A040977 (column 3), A133111 (column 4). Cf. A103905.
%K easy,nonn,tabl
%O 1,2
%A _Peter Bala_, Sep 18 2007
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