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A072888
Sum of the coefficients of the Schur function expansion of the square of the Vandermonde determinant in n variables.
2
-2, -14, 70, 910, -7280, -138320, 1521520, 38038000, -532532000
OFFSET
2,1
COMMENTS
The expansion is combinatorially explosive. The original output and further details are available from my website (see Links).
REFERENCES
T. Scharf, J.-Y. Thibon and B. G. Wybourne, Powers of the Vandermonde determinant ... J.Phys.A:Mat.Gen. (27) 4211 (1994)
FORMULA
I conjecture that a(n) = prod_{x=0..floor(n/2)} (-3x+1) * prod_{x=0..floor((n-1)/2)} (6x+1).
EXAMPLE
a(3) = -14 because V^2(x1,x2,x3) = {42} - 3{411} - 3{33} + 6{321} - 15{222}.
PROG
The expansions were evaluated using the program SCHUR.
CROSSREFS
Sequence in context: A258138 A206947 A203241 * A171012 A094583 A002058
KEYWORD
hard,sign
AUTHOR
Brian G Wybourne (bgw(AT)phys.uni.torun.pl), Jul 29 2002
STATUS
approved