A323977 Expansion of determinant of 6 X 6 matrix M_{u,v} = q^(maj(u*v^-1)) where u, v in S_3 and maj = MacMahon's major index (cf. A008302).

1, 0, -3, -4, 3, 12, 5, -12, -18, 0, 18, 12, -5, -12, -3, 4, 3, 0, -1

Offset: 0

Author

N. J. A. Sloane, Feb 10 2019

Keywords

• sign
• fini
• full

Links

• C. Krattenthaler, Advanced Determinant Calculus: A Complement, Linear Algebra Appl. 411 (2005), 68-166; arXiv:math/0503507v2 [math.CO], 2005. See Theorem 56.

Crossrefs

Cf. A008302, A323978, A323979.

Formula

G.f.: (1-q^2)^3*(1-q^3)^4.