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).

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

Jinyuan Wang, Table of n, a(n) for n = 0..144

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

Cf. A008302, A323977, A323979.

Sequence in context: A360619 A058203 A341297 * A219390 A050585 A050555

Adjacent sequences: A323975 A323976 A323977 * A323979 A323980 A323981

Keyword

sign,fini,full

Author

N. J. A. Sloane, Feb 10 2019

Status

approved