A072888 Sum of the coefficients of the Schur function expansion of the square of the Vandermonde determinant in n variables.

-2, -14, 70, 910, -7280, -138320, 1521520, 38038000, -532532000

Offset: 2

Author

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

Keywords

• hard
• sign

Comments

The expansion is combinatorially explosive. The original output and further details are available from my website (see Links).

Examples

			a(3) = -14 because V^2(x1,x2,x3) = {42} - 3{411} - 3{33} + 6{321} - 15{222}.
		

References

• T. Scharf, J.-Y. Thibon and B. G. Wybourne, Powers of the Vandermonde determinant ... J.Phys.A:Mat.Gen. (27) 4211 (1994)

Links

• 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).