# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a133112 Showing 1-1 of 1 %I A133112 #5 Sep 23 2024 05:07:28 %S A133112 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 A133112 64,1,8,84,672,2772,4224,1716,128,1,9,120,1386,9504,28314,27456,6435, %U A133112 256,1,10,165,2640,28314,151008,306735,183040,24310,512,1 %N A133112 Triangular array, read by rows, associated with sums of certain Vandermonde determinants. %C A133112 Appears to be the same as A073165 read as a triangular array (excluding the first column). %F A133112 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 A133112 Triangle starts: %e A133112 1; %e A133112 2 1; %e A133112 3 4 1; %e A133112 4 10 8 1; %e A133112 5 20 35 16 1; %Y A133112 A000292 (column 2), A040977 (column 3), A133111 (column 4). Cf. A103905. %K A133112 easy,nonn,tabl %O A133112 1,2 %A A133112 _Peter Bala_, Sep 18 2007 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE