A323977 -id:A323977 - cp's OEIS frontend

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

N. J. A. Sloane, Feb 10 2019

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.

Cf. A008302, A323977, A323979.

G.f.: (1-q^2)^12*(1-q^3)^16*(1-q^4)^18.

A323979 Expansion of determinant of 120 X 120 matrix M_{u,v} = q^(maj(u*v^-1)) where u, v in S_5 and maj = MacMahon's major index (cf. A008302).

Original entry on oeis.org

1, 0, -60, -80, 1680, 4704, -25660, -128640, 150420, 2062160, 2230548, -19194240, -63712740, 57664320, 724837020, 1055778256, -3865916310, -17164305600, -7987686380, 111558610080, 309981082824, -83708879920, -2310552888780, -4721178106560, 4129349973890, 39231750371520, 64807106219940, -86501225014320, -580167287063160, -840576756949440, 1330114847500228

Offset: 0

N. J. A. Sloane, Feb 10 2019

Jinyuan Wang, Table of n, a(n) for n = 0..1200
C. Krattenthaler, Advanced Determinant Calculus: A Complement, Linear Algebra Appl. 411 (2005), 68-166; arXiv:math/0503507v2 [math.CO], 2005. See Theorem 56.

Cf. A008302, A323977, A323978.

G.f.: (1-q^2)^60*(1-q^3)^80*(1-q^4)^90*(1-q^5)^96.

cp's OEIS Frontend

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).

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