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Search: id:A072888
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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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+0
3
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| -2, -14, 70, 910, -7280, -138320, 1521520, 38038000, -532532000
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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The expansion is combinatorially explosive. The original output is available from my website given above as well as further details.
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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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B G Wybourne, Title?
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FORMULA
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I conjecture that $$a(n)= \prod_{x=0}^{[n/2]}(-3x+1)\prod_{x=0}^{[(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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PROGRAM
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The expansions were evaluated using the programme SCHUR.
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CROSSREFS
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Sequence in context: A084132 A084770 A086243 this_sequence A094583 A002058 A095933
Adjacent sequences: A072885 A072886 A072887 this_sequence A072889 A072890 A072891
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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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