A323980 Expansion of determinant of 24 X 24 matrix M_{u,v} = q^(inv(u*v^-1)) where u, v in S_4 and inv is number of inversions.

1, -36, 630, -7148, 59193, -382032, 2004938, -8819856, 33292656, -109911296, 322501266, -852715008, 2055752147, -4563680868, 9404597538, -18107068172, 32737836213, -55804850136, 89956581256, -137430862056, 199259540514, -274319614896, 358419693312, -443688451632, 518556849207, -568577821788

Offset

0,2

Links

Jinyuan Wang, Table of n, a(n) for n = 0..72

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)^36*(1-q^3)^8*(1-q^6)^2.

Crossrefs

The analog for S_3 is (modulo signs) a row of A159255. For S_5 see A323981.

Sequence in context: A160316 A210432 A010952 * A287990 A283630 A035713

Adjacent sequences: A323977 A323978 A323979 * A323981 A323982 A323983

Keyword

sign,fini,full

Author

N. J. A. Sloane, Feb 11 2019

Status

approved