A323981 Expansion of determinant of 120 X 120 matrix M_{u,v} = q^(inv(u*v^-1)) where u, v in S_5 and inv is number of inversions.
1, -240, 28680, -2275340, 134824740, -6364768848, 249355900430, -8339136948960, 243023603409690, -6269722780034700, 144985184977092522, -3035621444374813800, 58027460699588712925, -1019806488183014948520, 16576321900226237215860, -250482543363917804395120, 3534533562046161990784275
Offset: 0
Links
- Jinyuan Wang, Table of n, a(n) for n = 0..600
- C. Krattenthaler, Advanced Determinant Calculus: A Complement, Linear Algebra Appl. 411 (2005), 68-166; arXiv:math/0503507v2 [math.CO], 2005. See Theorem 55.
Formula
G.f.: (1-q)^240*(1-q^3)^60*(1-q^6)^20*(1-q^10)^6.