%I A133111
%S A133111 0,0,0,1,16,126,672,2772,9504,28314,75504,184041,416416,884884,1782144,
%T A133111 3426384,6325632,11267532,19442016,32605881,53300016,85131970,133138720,
%U A133111 204246900,307850400,456528150,666928080,960846705,1366537536
%N A133111 a(n) = 1/(1!*2!*3!*4!)*sum {1 <= x_1, x_2, x_3, x_4 <= n} |det V(x_1,
               x_2,x_3,x_4)|, where V(x_1,x_2,x_3,x_4} is the Vandermonde matrix 
               of order 4.
%C A133111 Compare with A000292 and A040977 for the corresponding sums for the Vandermonde 
               matrices of order 2 and 3 respectively.
%C A133111 a(n)= sum of dimensions of all irreducible polynomial representations 
               of GL(4) whose highest weight is of the form (m1>=m2>=m3>=m4) and 
               m1<=n. - Oded Yacobi (oyacobi(AT)math.ucsd.edu), Jul 24 2008
%F A133111 a(n) = 1/288*sum {1 <= i,j,k,l <= n} |(i-j)(i-k)(j-k)(i-l)(j-l)(k-l)|. 
               G.f.: x^4*(1 + 5x + 5x^2 + x^3)/(1 - x)^11 . a(n) = n^2(n^2 - 1)^2(n^2 
               - 4)(n^2 - 9)/302400. a(n) = sum {i + j + k + l = n} i*j*k^2*l^3.
%t A133111 f[n_] := n^2 (n^2 - 1)^2 (n^2 - 4) (n^2 - 9)/302400; Array[f, 30] (* 
               or *) - Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007
%t A133111 Rest@ CoefficientList[ Series[x^4*(1 + 5 x + 5 x^2 + x^3)/(1 - x)^11, 
               {x, 0, 30}], x] - Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007
%Y A133111 Cf. A000292, A040977, A133112.
%Y A133111 Sequence in context: A000485 A007787 A067470 this_sequence A163399 A004017 
               A167471
%Y A133111 Adjacent sequences: A133108 A133109 A133110 this_sequence A133112 A133113 
               A133114
%K A133111 easy,nonn
%O A133111 1,5
%A A133111 Peter Bala (pbala(AT)toucansurf.com), Sep 13 2007
%E A133111 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007