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A323978
Expansion of determinant of 24 X 24 matrix M_{u,v} = q^(maj(u*v^-1)) where u, v in S_4 and maj = MacMahon's major index (cf. A008302).
3
1, 0, -12, -16, 48, 192, 116, -768, -1980, -496, 7092, 15360, 2636, -48192, -97044, -22864, 256002, 521280, 191908, -1096416, -2405376, -1290288, 3823524, 9570240, 6907098, -10634976, -32922540, -30209648, 21729096, 97815552, 110674724, -21257376, -249464409, -345423376, -63028416, 538288272, 927732396, 442024992, -948626520, -2154606896
OFFSET
0,3
LINKS
C. Krattenthaler, Advanced Determinant Calculus: A Complement, Linear Algebra Appl. 411 (2005), 68-166; arXiv:math/0503507v2 [math.CO], 2005. See Theorem 56.
FORMULA
G.f.: (1-q^2)^12*(1-q^3)^16*(1-q^4)^18.
CROSSREFS
KEYWORD
sign,fini,full
AUTHOR
N. J. A. Sloane, Feb 10 2019
STATUS
approved