|
Search: id:A133111
|
|
|
| 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. |
|
+0
4
|
|
| 0, 0, 0, 1, 16, 126, 672, 2772, 9504, 28314, 75504, 184041, 416416, 884884, 1782144, 3426384, 6325632, 11267532, 19442016, 32605881, 53300016, 85131970, 133138720, 204246900, 307850400, 456528150, 666928080, 960846705, 1366537536
(list; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
Compare with A000292 and A040977 for the corresponding sums for the Vandermonde matrices of order 2 and 3 respectively.
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
|
|
FORMULA
|
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.
|
|
MATHEMATICA
|
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
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
|
|
CROSSREFS
|
Cf. A000292, A040977, A133112.
Sequence in context: A000485 A007787 A067470 this_sequence A163399 A004017 A167471
Adjacent sequences: A133108 A133109 A133110 this_sequence A133112 A133113 A133114
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Peter Bala (pbala(AT)toucansurf.com), Sep 13 2007
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2007
|
|
|
Search completed in 0.002 seconds
|
