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

0,2

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.

Crossrefs

The analog for S_3 is (modulo signs) a row of A159255. For S_4 see A323980.

Sequence in context: A342306 A205256 A110163 * A258082 A269825 A232843

Adjacent sequences: A323978 A323979 A323980 * A323982 A323983 A323984

Keyword

sign,fini,full,look

Author

N. J. A. Sloane, Feb 11 2019

Status

approved