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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 (list; graph; refs; listen; history; text; internal format)
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)

LINKS

Table of n, a(n) for n=2..10.

B. G. Wybourne, Expansion of the Squares of the Vandermonde Determinant

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

Adjacent sequences:  A072885 A072886 A072887 * A072889 A072890 A072891

KEYWORD

hard,sign

AUTHOR

Brian G Wybourne (bgw(AT)phys.uni.torun.pl), Jul 29 2002

STATUS

approved

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Last modified February 24 11:39 EST 2018. Contains 299603 sequences. (Running on oeis4.)