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