A220790
Product(6^n - 6^k, k=0..n-1).
Original entry on oeis.org
1, 5, 1050, 8127000, 2273284440000, 22906523331216000000, 8310241106635054164480000000, 108537128570336598656772717772800000000, 51032497739317419104816901041614046625792000000000
Offset: 0
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[1] cat [&*[(6^n - 6^k): k in [0..n-1]]: n in [1..8]]; // Bruno Berselli, Jan 28 2013
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/* By the second formula: */
m:=9;
A109354 := [6^(n*(n-1) div 2): n in [0..m-1]];
A027873 := [1] cat [&*[6^i-1: i in [1..n]]: n in [1..m]];
[A109354[i]*A027873[i]: i in [1..m]]; // Bruno Berselli, Jan 30 2013
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Table[Product[6^n - 6^k, {k, 0, n-1}], {n, 0, 60}]
A086778
Number of n X n matrices over GF(5) with rank n-1.
Original entry on oeis.org
1, 144, 461280, 36211968000, 70794513504000000, 3457427279866560000000000, 4220654362961578542000000000000000, 128805138489674665490472000000000000000000000
Offset: 1
Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 03 2003
A335384
Order of the finite groups GL(m,q) [or GL_m(q)] in increasing order as q runs through the prime powers.
Original entry on oeis.org
6, 48, 168, 180, 480, 2016, 3528, 5760, 11232, 13200, 20160, 26208, 61200, 78336, 123120, 181440, 267168, 374400, 511056, 682080, 892800, 1014816, 1488000, 1822176, 2755200, 3337488, 4773696, 5644800, 7738848, 9999360, 11908560, 13615200, 16511040, 19845936, 24261120, 25048800, 28003968
Offset: 1
a(1) = #GL(2,2) = (2^2-1)*(2^2-2) = 3*2 = 6 and the 6 elements of GL(2,2) that is isomorphic to S_3 are the 6 following 2 X 2 invertible matrices with entries in F_2:
(1 0) (1 1) (1 0) (0 1) (0 1) (1 1)
(0 1) , (0 1) , (1 1) , (1 0) , (1 1) , (1 0).
a(2) = #GL(2,3) = (3^2-1)*(3^2-3) = 8*6 = 48.
a(3) = #GL(3,2) = (2^3-1)*(2^3-2)*(2^3-2^2) = 168.
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
- Daniel Perrin, Cours d'Algèbre, Maths Agreg, Ellipses, 1996, pages 95-115.
Cf.
A002884 [GL(m,2)],
A053290 [GL(m,3)],
A053291 [GL(m,4)],
A053292 [GL(m,5)],
A053293 [GL(m,7)],
A052496 [GL(m,8)],
A052497 [GL(m,9)],
A052498 [GL(m,11)].
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