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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.
2
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
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
KEYWORD
sign,fini,full
AUTHOR
N. J. A. Sloane, Feb 11 2019
STATUS
approved